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}.

Solution

Detailed Solution

Return to Sample Exam

@@ 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 <math>n</math>th derivative <math>f^{(n)}(x)</math> of <math>f</math> and then find <math>f'(3).</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>
-::<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
+<span class="exam">(b) Find the Taylor series for &nbsp;<math style="vertical-align: -5px">f(x)</math>&nbsp; at &nbsp;<math style="vertical-align: -5px">x_0=3,</math>&nbsp; i.e. write &nbsp;<math style="vertical-align: -5px">f(x)</math>&nbsp; in the form
-::::<math>f(x)=\sum_{n=0}^\infty a_n(x-3)^n.</math>
+::<math>f(x)=\sum_{n=0}^\infty a_n(x-3)^n.</math>
-{| class="mw-collapsible mw-collapsed" style = "text-align:left;"
+<hr>
-!Foundations: &nbsp;
+[[009C Sample Final 3, Problem 5 Solution|'''<u>Solution</u>''']]
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+[[009C Sample Final 3, Problem 5 Detailed Solution|'''<u>Detailed Solution</u>''']]
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-|&nbsp;&nbsp; '''(a)'''
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-|&nbsp;&nbsp; '''(b)'''
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 [[009C_Sample_Final_3|'''<u>Return to Sample Exam</u>''']]

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

Latest revision as of 16:20, 3 December 2017

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