Approximating a function with a Taylor Polynomial More free lessons at: http://www.khanacademy.org/video?v=8SsC5st4Ln In calculus, Taylor's theorem gives an approximation of a k-times differentiable function around a given point by a polynomial of degree k, called the kth-order Taylor polynomial. For a smooth function, the Taylor polynomial is the truncation at the order k of the Taylor series of the function. The first-order Taylor polynomial is the linear approximation of the function, and the second-order Taylor polynomial is often referred to as the quadratic approximation. There are several versions of Ta Taylorův polynom. Taylorův polynom tedy aproximuje hodnoty funkce , která má v daném bodě derivaci , pomocí polynomu , jehož koeficienty závisí na derivacích funkce v tomto bodě. Řada je pojmenována po anglickém matematikovi Brooku Taylorovi , který ji publikoval v roce 1712, avšak metoda aproximace funkce mocninnou řadou byla objevena již roku 1671 Jamesem Gregorym Taylorův polynom se používá k polynomiální aproximaci funkcí, protože platí, že všechny derivace Taylorova polynomu až do stupně n mají ve středu polynomu stejné funkční hodnoty jako odpovídající derivace funkce f. Tato aproximace je na okolí bodu a tím přesnější, čím vyšší stupeň polynomu použijeme. Zároveň platí, že se chyba se vzdáleností od středu zvyšuje Dobrý den, děkuji za upozornění, už jsem to opravil (musíte si vymazat cache) :) jinak jsem moc rád že se Vám videa líbí, děkuji mnohokrát

TAYLORÙV POLYNOM FUNKCE JEDNÉ PROMÌNNÉ Napite Taylorøv polynom stupnì funkce f stupnì n v bodì x0: 1. f(x) = ln(1 ¡ x), x0 = 0, n = 4 [T4(x) = ¡x ¡ x 2. * ZÁKLADNÍ KURZY \ Matematika II \ Diferenciál a Taylorův polynom \ DIFERENCIÁL A TAYLOROVA VĚTA *. STUDIJNÍ TEXT. ŘEŠENÉ PŘÍKLADY. Neřešené příklady - diferenciál funkce 2016. NEŘEŠENÉ PŘÍKLADY - tečná rovina, Taylorův

** Härledning av taylorpolynom**. Taylorutvecklingen av en funktion vilar på den så kallade analysens fundamentalsats, som förenar de två begreppen derivata och integral av en funktion: f ( x ) = f ( a ) ⏟ 0 : t e o r d n i n g e n s T a y l o r p o l y n o m + ∫ a x f ′ ( y 1 ) d y 1 ⏟ R e s t t e r m Polynom p tedy musí obsahovat hodnoty těchto derivací, navíc členy musí obsahovat (x-a), aby se vynulovaly po dosazení a. Členy polynomu musí také mít jmenovatele, který se při derivování bude krátit s exponenty, které se derivováním snižují o 1. Ve jmenovateli by měl být součin těchto exponentů, tedy faktoriál Taylor and Maclaurin (Power) Series Calculator The calculator will find the Taylor (or power) series expansion of the given function around the given point, with steps shown. You can specify the order of the Taylor polynomial. If you want the Maclaurin polynomial, just set the point to 0 Heute versuchen wir mittels eines mehrdimensionalen Taylor-Polynoms eine gute Nährung von Wurzel 0.9^1.1 zu bestimmen

Free Taylor/Maclaurin Series calculator - Find the Taylor/Maclaurin series representation of functions step-by-ste Example of a calculating a second-degree multivariable Taylor polynomial. Calculate the second-degree Taylor polynomial of \begin{align*} f(x,y) = e^{-(x^2+y^2)} \end{align*} at the point $(0,0)$ and at the point $(1,2) * Yao Zhao, Mark A*. Stadtherr, in Computer Aided Chemical Engineering, 2012. 3.2 Taylor models. For a real function f (y) over y ∈ Y, a Taylor model T f = (p f, R f), consisting of a q-th order Taylor polynomial in y around some y 0 ∈ Y and an interval remainder bound R f, can be constructed so that f ∈ T f for all y ∈ Y.This can be done using the Taylor theorem and/or by using Taylor. What Is a Taylor Polynomial? Let's start with the definition. Given a function f, a specific point x = a (called the center), and a positive integer n, the Taylor polynomial of f at a, of degree n.

To calculate the Taylor polynomial of degree \(n\) for functions of two variables beyond the second degree, we need to work out the pattern that allows all the partials of the polynomial to be equal to the partials of the function being approximated at the point \((a,b)\), up to the given degree approximation by a linear polynomial of f(x,y)nearthepoint(0,0). It's natural to ask if we can get a better approximation if we use a quadratic polynomial. It turns out that we can. The quadratic approximation of f(x,y)nearthegeneralpoint(a,b) is given b polynomial, but rather an infinite polynomial, (called a power series). Figure 1 shows the graphs of these approximations, together with the graph of f(x) = 1 1-x - 1. Figure 1 Notice how the graphs of the successive approximations get closer and closer to the curve near x = 0, but nowhere near the curve when x > 1 Which also proves that such a polynomial does exist, obviously you understood the proof and you know he's proving existence, but I'm not, so how did you realize that this proof proves existence? Thanks. $\endgroup$ - David Robert Jones Apr 10 '12 at 13:1 ** A Taylor polynomial approximates the value of a function, and in many cases, it's helpful to measure the accuracy of an approximation**. This information is provided by the Taylor remainder term: f(x) = Tn(x) + Rn(x) Notice that the addition of the remainder term Rn(x) turns the approximation into an equation. Here's the formula for [

And this polynomial right over here, this Nth degree polynomial centered at a, f or P of a is going to be the same thing as f of a. And you can verify that because all of these other terms have an x minus a here. So if you put an a in the polynomial, all of these other terms are going to be zero. And you'll have P of a is equal to f of a The Nth-order Maclaurin polynomial for y = f(x) is just the Nth-order Taylor polynomial for y = f(x) at x 0 = 0 and so it is p N(x) = XN n=0 f(n)(0) n! xn: De nition 2. 1 The Taylor series for y = f(x) at x 0 is the power series: P 1(x) = f(x 0) + f0(x 0)(x x 0) + f00(x 0) 2! (x x 0)2 + + f(n)(x 0) n! (x x 0)n + ::: (open form) which can also.

Taylor's Theorem - Integral Remainder Theorem Let f : R → R be a function that has k + 1 continuous derivatives in some neighborhood U of x = a ALA-b Taylors formel 2 Uppgift29.7 Write down the Taylor polynomial of order n for ln(x) in x=1. Vianv˜ander formelnf˜or Taylorpolynomet.Manharat

- The
**Taylor**series of a function is extremely useful in all sorts of applications and, at the same time, it is fundamental in pure mathematics, specifically in (complex) function theory. Recall that, if. - Example 7 In this example we'll evaluate the harder limit lim x→0 cosx− 1+ 1 2 xsinx [ln(1+ x)]4 Using Examples 2 and 4, lim x→0 cosx− 1+ 1 2 xsinx [ln(1+x)]4 = li
- Taylor's Remainder Theorem says that any smooth function can be written as an n th degree Taylor polynomial plus a function that is of order n + 1 near x = c. Taylor's Remainder Theorem If f is smooth from a to b , let P n (x) be the n th degree Taylor polynomial at x = c , then for every x there is a z between x and c wit
- such polynomial exists follows by a dimension counting argument in linear algebra. But we will need the explicit expression of the polynomial, so let's construct the polynomial explicitly. Indeed, let f be as in Theorem 1. Let P(x) = Xn k=0 a k(x a)k: (This is a convenient form of expressing a polynomial of degree k, since we will need to comput
- Taylor's Inequality. Taylor's inequality is an estimate result for the value of the remainder term in any -term finite Taylor series approximation.. Indeed, if is any function which satisfies the hypotheses of Taylor's theorem and for which there exists a real number satisfying on some interval, the remainder satisfie
- Worked out problems; Example 1: Solve the initial value problem y' = -2xy 2, y(0) = 1 for y at x = 1 with step length 0.2 using Taylor series method of order four.: Solution: Example 2: Using Taylor series method of order four solve the initial value problem y' = (x - y)/2, on [0, 3] with y(0) = 1
- Chapter 4: Taylor Series 17 same derivative at that point a and also the same second derivative there. We do both at once and deﬁne the second degree Taylor Polynomial for f (x) near the point x = a. f (x) ≈ P 2(x) = f (a)+ f (a)(x −a)+ f (a) 2 (x −a)2 Check that P 2(x) has the same ﬁrst and second derivative that f (x) does at the point x = a. 4.3 Higher Order Taylor Polynomial

Find the Taylor series expansion of any function around a point using this online calculator Taylor's Series of sin x In order to use Taylor's formula to ﬁnd the power series expansion of sin x we have to compute the derivatives of sin(x) MATH142-TheTaylorRemainder JoeFoster Practice Problems EstimatethemaximumerrorwhenapproximatingthefollowingfunctionswiththeindicatedTaylorpolynomialcentreda In Mathematics, the Taylor series is the most famous series that is utilized in several mathematical as well as practical problems. The Taylor theorem expresses a function in the form of the sum of infinite terms. These terms are determined from the derivative of a given function for a particular point. The standard definition of an algebraic function is provided using an algebraic equation OBTAINING TAYLOR FORMULAS Most Taylor polynomials have been bound by other than using the formula pn(x)=f(a)+(x−a)f0(a)+ 1 2! (x−a)2f00(a) 1 n! (x−a)nf(n)(a) because of the diﬃculty of obtaining the derivative

Let us call the difference between the polynomial Pn (x) and f(x), the remainder, that is, f (x) =Pn (x) +Rn (x) (10.6) If Rn (x) is small, then Pn (x) is a good approximation for f(x). Indeed, we could derive the Taylor formula as an approximation of the difference between f(x) and f(a). Geometrically, we could try to approximate the segment. The Taylor Polynomial 9.1 Introduction Let f be a function and let F be a collection of nice functions. The approximation problem is simply to find a function g ∈ F that is close to the given function f . There are two issues immediately. How is the collection F selected, and what do we mean b Taylor Series Calculator is a free online tool that displays the Taylor series for the given function and the limit. BYJU'S online Taylor series calculator tool makes the calculation faster, and it displays the series in a fraction of seconds The MATLAB command for a Taylor polynomial is taylor(f,n+1,a), where f is the function, a is the point around which the expansion is made, and n is the order of the polynomial. We can use the following code: >>syms x >>f=inline('sin(x)') f = Inline function: f(x) = sin(x) >>taylor(f(x),2,0) ans = x >>taylor(f(x),4,0) ans = x-1/6*xˆ3.

* Converting a Taylor series to a polynomial • The general series command : see the taylor/details help page*. See Also. mtaylor. series Download Help Document ? [] About Us. Maplesoft™, a subsidiary of Cybernet Systems Co. Ltd. in Japan, is the leading provider of high-performance software tools for engineering, science, and mathematics.. Taylor series expansion of symbolic expressions and functions. Select a Web Site. Choose a web site to get translated content where available and see local events and offers 9.(Just for fun pts.) Find polynomial approximations to the following functions near zero by multiplying, dividing by, integrating or di erentiating polynomial approximations to well known functions. If you have a calculator, graph the function and the polynomial to see how accurate the approximation is. Note that the higher the degree of you

- Taylor Series are studied because polynomial functions are easy and if one could find a way to represent complicated functions as series (infinite polynomials) then one can easily study the properties of difficult functions. Evaluating definite Integrals: Some functions have no antiderivative which can be expressed in terms of familiar.
- Get the free Log(1-x) Taylor Series widget for your website, blog, Wordpress, Blogger, or iGoogle. Find more Mathematics widgets in Wolfram|Alpha
- It gives a polynomial expansion for every smooth function f. We just need to calculate the first n derivatives of f, evaluate them at c, divide each one by n!, and sum up these terms
- The coefficient \(\dfrac{f(x)-f(a)}{x-a}\) of \((x-a)\) is the average slope of \(f(t)\) as \(t\) moves from \(t=a\) to \(t=x\text{.}\) We can picture this as the.

Generally speaking, a higher-degree polynomial results in a better approximation. For the value of e x when x is near 100, you get a good estimate by using a Taylor polynomial for e x with a = 100:. To sum up, remember the following: A convergent Taylor series expresses the exact value of a function ** Describe the procedure for finding a Taylor polynomial of a given order for a function**. Explain the meaning and significance of Taylor's theorem with remainder. Estimate the remainder for a Taylor series approximation of a given function

Taylor Series Expansion Calculator computes a Taylor series for a function at a point up to a given power. Taylor series is a way to representat a function as a sum of terms calculated based on the function's derivative values at a given point as shown on the image below Taylor series expansions of logarithmic functions and the combinations of logarithmic functions and trigonometric, inverse trigonometric, hyperbolic, and inverse hyperbolic functions

1 Derivation of Taylor Series Expansion Objective: Given f(x), we want a power series expansion of this function with respect to a chosen point xo, as follows: (1) (Translation: find the values of a0, a1, a2, of this infinite series so that the equation holds. Method: The general idea will be to process both sides of this equation and choose values of x so that only on Here, n is a whole number. Each coefficient a 0, a 1, a 2, , a n, must be constant.Furthermore, we always insist that a n is nonzero. (Otherwise, we really wouldn't have an nth term at all, right?)Then we say that the degree of the polynomial is n.. Often, you'll see the terms written in the opposite order, from high degree down to low, which is called standard form

- dict.cc | Übersetzungen für 'Taylor-Polynom' im Englisch-Deutsch-Wörterbuch, mit echten Sprachaufnahmen, Illustrationen, Beugungsformen,.
- Main Idea: The Lagrange interpolating polynomial, P n(x), has been deﬁned so that the polynomial agrees with the original function f(x) at n+ 1 distinct input values x0,x1,··· ,x n. On the other hand, Taylor polynomials approximate a function using a single center point at which we know the value of the function and the value o
- g up to n = 5. The two points about which we will look at are.
- If the third argument n is present then it specifies the ``truncation order'' of the series. The concept of ``truncation order'' used is ``total degree'' in the variables. If n is not present, the truncation order used is the value of the global variable Order, which is 6 by default
- Explanation of Each Step Step 1. Maclaurin series coefficients, a k can be calculated using the formula (that comes from the definition of a Taylor series) where f is the given function, and in this case is sin(x).In step 1, we are only using this formula to calculate the first few coefficients

Thus, to nd the kth order Taylor polynomial of fg, simply multiply the kth Taylor poly-nomials of f and g together, discarding all terms of degree > k. Example 1. What is the 6th order Taylor polynomial of x3ex? Solution: x3ex = x3 1 + x+ x2 2 + x3 6 + o(x3) = x3 + x4 + x5 2 + x6 6 + o(x6); so the answer is x3 + x4 + 1 2 x5 + 1 6 x6 To find a polynomial approximation to a function, just use this expression but let n range up to the desired degree instead of all the way to infinity. This device cannot display Java animations. The above is a substitute static image See About the calculus applets for operating instructions. 1. For a cosine functio

** Example Compute the third Taylor polynomial of f(x) = ex at a = 0**. 3 Solution Write p(x) = c 0 + c 1x + c 2x2 + c 3x3.We need to ﬁnd c 0, c 1, c 2, and c 3 so that p(i)(0) = f(i)(0) for i = 0, 1, 2, and 3. In our case f(i)(x) = ex for all i ≥ 0 and e0 = 1. So, f(i)(0) = 1 for all i. We compute p0(x) = c 1 +2c 2x +3c 3x2, p00(x) = 2c 2 +6c 3x, and p000(x) = 6c This preview shows page 2 - 7 out of 14 pages.. 1. Taylor's theorem a) (10 marks) Present the Taylor's polynomial of degree two, in the matrix form for the function f (x, y) = e x-1 (y-2) + y 2 near the point a = (1, 2), and then use it to approximate the value of a) (10 marks) Present the Taylor's polynomial of degree two, in the matrix form for the function

The Taylor polynomial of degree 6 about x = 3 for f (x) does not exist. c) The remainder term R 5 (x) for f (x) is equal to zero. d) The remainder term R 3 (x) for f (x) is equal to zero. e) The remainder term R 3 (2) for f (x) is equal to 32. There is at least one mistake. For example, choice (a) should be True nth derivative test for the nature of stationary points Suppose that f has a stationary point at a and that f0(a) = ··· = f(n−1)(a) = 0, while f(n)(a) 6= 0.If f(n) is continuous then (1) if n is even and f(n)(a) > 0 then f has a local minimum at a, (2) if n is even and f(n)(a) < 0 then f has a local maximum at a, (3) if n is odd then f has a point of inﬂection at a

- Taylor Series SingleVariable and Multi-Variable • Single variable Taylor series: Let f be an inﬁnitely diﬀerentiable function in some open interval around x= a
- Taylors Polynomial Codes and Scripts Downloads Free. This algorithm factors a polynomial but will only factor it by giving the rational roots. This implements polynomial functions over a single variable in Python
- Program on sum of taylor series in C language. Sum of Taylor Series Program. Below is a program on sum of taylor series. (n+1)th term of taylor series is given by (x^n)/n!, where series starts with 1.. #include<stdio.h> #include<math.h> int main() { printf(\n\n\t\tStudytonight - Best place to learn\n\n\n); int x,i; int fact = 1,n; float sum=0; printf(\n\nEnter the value of x in the series.
- I have a problem in Octave to solve but I can't get to beat it. I have to compute the taylor series of the exponential function with x=1 and the factorial has to be an extra function (self defined..
- You can get the 3rd degree Taylor polynomial by just dropping the terms of degree 4 or higher: 4a^3(x-a)+ 6a^2(x- a)^2+ 4a(x- a)^3. Since the Taylors series for a polynomial is just that polynomial shifted, we can also get this by letting y= x-a so that a= y+a
- Online calculator finds Taylor or Maclaurin series expansion of the input functio
- A Taylor series is an idea used in computer science, calculus, chemistry, physics and other kinds of higher-level mathematics.It is a series that is used to create an estimate (guess) of what a function looks like. There is also a special kind of Taylor series called a Maclaurin series.. The theory behind the Taylor series is that if a point is chosen on the coordinate plane (x-and y-axes.

Comments . Transcription . Taylor-polynom fourth and sixth order Taylor polynomial approximations of f. Plot f and the four polynomials on the same graph. If you look at equation (5), we realize that we need f and a bunch of its derivatives evaluated at x =0. To accomplish this, we construct the following table. n f(n)(x) f(n)(0) 0 sinx 0 1 cosx 1 2 −sinx

Find an approximated value for \sqrt[ ]{9.03} using a Taylors polynomial of third degree and estimate the error. I thought of solving it by using.. is given in the table below for the first few . k expansion simplified at a = 0 0: f (a) (1 + a) 1 / 21: 1: f ′ (a) (x-a): 1 2 (1 + a)-1 / 2 (x-a): 1 2 x: 2: f (2) (a) 2! (x-a) 2-1 8 (1 + a)-3 / 2 (x-a) 2-1 8 x 23: f (3) (a) 3! (x-a) 3: 3 48 (1 + a)-5 / 2 (x-a) 3: 1 16 x 3: 4: f (4) (a) 4! (x-a) 4-15 384 (1 + a)-7. Problem Set#1 . Multiple Choice Test . Chapter 01.07 Taylors Series Revisited . COMPLETE SOLUTION SET . 1. The coefficient of the . x5 term in the Maclaurin polynomial for . sin (2. x) is (A) 0 (B) 0.008333 Taylor series, in mathematics, expression of a function f—for which the derivatives of all orders exist—at a point a in the domain of f in the form of the power series Σ ∞n = 0 f (n) (a) (z − a)n/n! in which Σ denotes the addition of each element in the series as n ranges from zero (0) to infinit

Taylor polynomial of a matrix function. The remaining sections of this paper are organized as follows. In section 2 we state and prove the remainder term for the kth-degree Taylor polynomial of a matrix function. In section 3 we investigate some applications of this result by bounding the rst order remainder term using pseudospectral technique 12. 4 pt Find the Taylor's polynomial T 3 (x) of order 3 of function f (x) = 2 sin 3 x centered at a = π. Be sure to simplify all coefficients. You may use the derivatives given below: f 0 (x) = 6 cos 3 x f 00 (x) =-18 sin 3 x f 000 (x) =-54 cos 3 x You have now reached the end of the exam. Please scan and submit a SINGLE PDF file to the. polynomial. Repeating this for the ﬁrst degree approximation, we might expect: f(b) = f(a) + f (a)(b − a) + f (c) (b − a)2 2 for some c in (a, b). The term in square brackets is precisely the linear approximation. Question: Guess the formula for the diﬀerence between f(b) and its n-th order Taylor polynomial at x = a ( Translation: find the values of a 0, a 1, of this infinite series so that the equation holds. Method: The general idea will be to process both sides of this equation and choose values of x so that only one unknown appears each time.. To obtain a o: Choose x=x o in equation (1). This results in a 0 = f(x o). To obtain a 1: First take the derivative of equation (1 Mika Seppälä: Solved Problems on Taylor and Maclaurin Series TAYLOR AND MACLAURIN SERIES Taylor Series of a function f at x = a is f()k ()a k! ()x a k k=0 It is a Power Series centered at a. Maclaurin Series of a function f is a Taylor Series at x = 0

- 1)Find the 3rd order Taylor polynomial P3(x) in powers of x for the function f(x)=e^(-4x), and, using the Lagrange formula for the remainder, write the remainder R3(x) as a function of x and c. 2)Find the 3rd order Taylor polynomial P3(x) in powers of x for the function f(x)=3/(1+x), and, using the Lagrange formula for the remainder, write the remainder R3(x) as a function of x and c. 3)Find.
- Many functions can be written as a power series. The archetypical example is provided by the geometric series: . which is valid for -1<x<1. If we write a function as a power series with center , we call the power series the Taylor series of the function with center . (When the center is , the Taylor series is also often called the McLaurin series of the function.
- Other articles where Polynomial interpolation is discussed: numerical analysis: Historical background: a set of data (polynomial interpolation). Following Newton, many of the mathematical giants of the 18th and 19th centuries made major contributions to numerical analysis. Foremost among these were the Swiss Leonhard Euler (1707-1783), the French Joseph-Louis Lagrange (1736-1813.
- This website uses cookies to improve your experience while you navigate through the website. Out of these, the cookies that are categorized as necessary are stored on your browser as they are essential for the working of basic functionalities of the website
- A blog about Statistics, Data Science and Machine Learning experiments using Python, R and Java. On occasion Finance, Electrical circuits and Arduin
- Taylor expansion - series experiments with Matlab Once you know how Maclaurin series work, Taylor series are easier to understand. Taylor expansions are very similar to Maclaurin expansions because Maclaurin series actually are Taylor series centered at x = 0. Thus, a Taylor series is a more generic form of the Maclaurin series, and it can be centered at any x-value

- The Taylor series linearization (TSL) method is used with variance estimation for statistics that are vastly more complex than mere additions of sample values
- Taylor series expansions of inverse trigonometric functions, i.e., arcsin, arccos, arctan, arccot, arcsec, and arccsc
- In Wickens' Macroeconomic Theory book, in page 48(1st edition), the author states that by doing a
**taylor**approximation we get the following result. Why is that? What approximation did he use? I've.. - g. Exempel meningar med Taylor polynomial, översättning
- Taylor Polynomial of Ln (x) Thread starter xtrubambinoxpr; Start date Nov 17, 2013; Nov 17, 2013 #1 xtrubambinoxpr. 87 0. I need help understanding why the ln (x) taylor polynomial is (x-1)-1/2(x-1)^2.... + etc. I cannot grasp the concept.. Answers and Replies Related.
- Learn math Krista King May 26, 2019 math, learn online, online course, online math, calculus 2, calculus ii, calc 2, calc ii, sequences, series, radius of convergence, interval of convergence, radius and interval of convergence, taylor series, power series, power series representation, nth degree taylor polynomial, terms of the taylor.

- Taylor - Free download as PDF File (.pdf), Text File (.txt) or read online for free
- Looks pretty much like the sin function. Problems. Exercise: Show that is approximated to within 7 decimals by for all x in. Exercise: Use taylor and convert(..,polynom) to compute and plot, on the interval specified, the first few taylor polynomials of the following functions. Observe the convergence of the polynomials to the function and make comments
- Taylor's Theorem and The Lagrange Remainder. We are about to look at a crucially important theorem known as Taylor's Theorem. Before we do so though, we must look at the following extension to the Mean Value Theorem which will be needed in our proof

Taylor's Series of a Polynomial Item Preview podcast_ocw-scholar-single-variable-c_taylors-series-polynomia_1000346212048_itemimage.png . remove-circle Share or Embed This Item. Learning Objectives. 6.3.1 Describe the procedure for finding a Taylor polynomial of a given order for a function.; 6.3.2 Explain the meaning and significance of Taylor's theorem with remainder.; 6.3.3 Estimate the remainder for a Taylor series approximation of a given function Let f be a function that has derivatives of all orders for all real numbers. Assume f(1)=3, f'(1)=-2, f(1)=2, and f'''(1)=4 a. Write the second-degree Taylor polynomial for f about x=1 and use it to approximate f(0.7). b. Write the third-degree Taylor polynomial for f about x=1 and use it..