Difference between revisions of "009C Sample Final 3, Problem 5"

Latest revision as of 16:20, 3 December 2017

Consider the function

f(x)=e^{-{\frac {1}{3}}x}.

(a) Find a formula for the $n$ th derivative $f^{(n)}(x)$ of $f$ and then find $f'(3).$

(b) Find the Taylor series for $f(x)$ at $x_{0}=3,$ i.e. write $f(x)$ in the form

f(x)=\sum _{n=0}^{\infty }a_{n}(x-3)^{n}.

@@ Line 1: / Line 1: @@
 <span class="exam"> Consider the function
-::<math>f(x)=e^{-\frac{1}{3}x}</math>
+::<math>f(x)=e^{-\frac{1}{3}x}.</math>
 <span class="exam">(a) Find a formula for the &nbsp;<math>n</math>th derivative &nbsp;<math style="vertical-align: -5px">f^{(n)}(x)</math>&nbsp; of &nbsp;<math style="vertical-align: -5px">f</math>&nbsp; and then find &nbsp;<math style="vertical-align: -5px">f'(3).</math>