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

Revision as of 11:52, 18 February 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}.

Solution:

(a)

Step 2:

(b)

Step 2:

Final Answer:
(a)
(b)

@@ Line 1: / Line 1: @@
-<span class="exam">Compute
+<span class="exam"> Consider the function
-::<span class="exam">a) <math style="vertical-align: -12px">\lim_{n\rightarrow \infty} \frac{3-2n^2}{5n^2+n+1}</math>
+::::<math>f(x)=e^{-\frac{1}{3}x}</math>
-::<span class="exam">b) <math style="vertical-align: -12px">\lim_{n\rightarrow \infty} \frac{\ln n}{\ln 3n}</math>
+::<span class="exam">a) Find a formula for the <math>n</math>th derivative <math>f^{(n)}(x)</math> of <math>f</math> and then find <math>f'(3).</math>
+::<span class="exam">b) Find the Taylor series for <math>f(x)</math> at <math>x_0=3,</math> i.e. write <math>f(x)</math> in the form
+::::<math>f(x)=\sum_{n=0}^\infty a_n(x-3)^n.</math>
 {| class="mw-collapsible mw-collapsed" style = "text-align:left;"