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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

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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

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