💬 👋 We’re always here. Join our Discord to connect with other students 24/7, any time, night or day.Join Here!
Get the answer to your homework problem.
Try Numerade free for 7 days
Like
Report
Find the Taylor polynomial of degree $n$ centered at the number $a$$f(x)=e^{x}, \quad n=3, \quad a=0$
$T_{3}(x)=f(a)+f^{\prime}(a)(x-a)+f^{\prime \prime}(a) \frac{(x-a)^{2}}{2 !}+f^{\prime \prime \prime}(a) \frac{(x-a)^{3}}{3 !}=1+x+\frac{x^{2}}{2}+\frac{x^{3}}{6}$
Calculus 1 / AB
Chapter 3
Derivatives
Section 8
Linear Approximations and Taylor Polynomials
Oregon State University
University of Nottingham
Idaho State University
Boston College
Lectures
03:09
In mathematics, precalculu…
31:55
In mathematics, a function…
02:04
Find the Taylor polynomial…
01:38
01:23
01:50
02:23
Finding a Taylor Polynomia…
03:53
01:28
05:01
02:18
05:30
a. Find the nth-order Tayl…
07:20
03:29
05:14
08:44
02:02
09:47
02:42
03:57
04:08
06:39
this question asked us to find the tailor Paul. No meal. First things first half of a we know we have e to the X. We can consider X to B R A, which is zero either. The first powers warm now F prime of X is the same thing. It's simply eating the X therefore off, prime Eh is also wants the same thing. A double prime, same thing you did the axe. Therefore, after the prime of a is one, you can probably see a pattern off. Triple Prime of X is also eating the X they're for after Apple. Prime of acts is also one. It's the same thing. It's either zero, which is one. Therefore, we know that we can write out our final equation as after they plus of prime of a Times X, minus a plus after work from eight times X minus a squared over two factorial, plus a triple prime of a X minus a cubed over three factorial
View More Answers From This Book
Find Another Textbook
In mathematics, precalculus is the study of functions (as opposed to calculu…
In mathematics, a function (or map) f from a set X to a set Y is a rule whic…
Find the Taylor polynomial of degree $n$ centered at the number $a$.$f(x…
Find the Taylor polynomial $p_{3}$ centered at $a=e$ for $f(x)=\ln x$.
Find the Taylor polynomials $p_{3}$ and $p_{4}$ centered at $a=0$ for $f(x)=…
Finding a Taylor Polynomial In Exercises $27-32,$ find the $n$ th Taylor pol…
Find the Taylor polynomial $T_{3}(x)$ for the function $f$ centered at the n…
Find the Taylor polynomials $p_{1}, p_{2},$ and $p_{3}$ centered at $a=1$ fo…
Find the Taylor polynomials $p_{1}, \ldots, p_{5}$ centered at $a=0$ for $f(…
a. Find the nth-order Taylor polynomials for the given function centered at …
a. Find the nth-order Taylor polynomials of the given function centered at $…
Find the Taylor polynomials $ T_3(x) $ for the function $ f $ centered at th…
04:22
Find the derivative of the function. Simplify wherepossible. $$y=\ar…
02:59
$$\begin{array}{l}{\text { Radiometric dating Scientists can determine t…
02:55
(a) What is wrong with the following equation? $\frac{x^{2}+x-6}{x-2}=x+3$
04:29
$11-20$(a) Find the intervals on which $f$ is increasing or decreasing.<…
04:16
$32-34$(a) Use the definition of the derivative to calculate $f^{\prime}…
02:34
Find an equation of the tangent line to the curve at the given point. Illust…
00:24
$$\begin{array}{l}{\text { Use the graph of } f \text { to estimate the …
01:04
Find the parabola with equation $y=a x^{2}+b x$ whose tangent line at $(1,1)…
03:04
Find the limit. Use l'Hospital's Rule where appropriate. If there …
04:38
