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| | <span class="exam">(b) <math style="vertical-align: -15px">a_n=\cos(n\pi)\bigg(\frac{1+n}{n}\bigg)^n</math> | | <span class="exam">(b) <math style="vertical-align: -15px">a_n=\cos(n\pi)\bigg(\frac{1+n}{n}\bigg)^n</math> |
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| − | {| class="mw-collapsible mw-collapsed" style = "text-align:left;"
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| − | !Foundations:
| + | [[009C Sample Final 3, Problem 1 Solution|'''<u>Solution</u>''']] |
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| − | |'''L'Hôpital's Rule''' | |
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| − | Suppose that <math style="vertical-align: -11px">\lim_{x\rightarrow \infty} f(x)</math> and <math style="vertical-align: -11px">\lim_{x\rightarrow \infty} g(x)</math> are both zero or both <math style="vertical-align: -1px">\pm \infty .</math>
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| − | If <math style="vertical-align: -19px">\lim_{x\rightarrow \infty} \frac{f'(x)}{g'(x)}</math> is finite or <math style="vertical-align: -4px">\pm \infty ,</math>
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| − | then <math style="vertical-align: -19px">\lim_{x\rightarrow \infty} \frac{f(x)}{g(x)}\,=\,\lim_{x\rightarrow \infty} \frac{f'(x)}{g'(x)}.</math>
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| − | '''Solution:''' | + | [[009C Sample Final 3, Problem 1 Detailed Solution|'''<u>Detailed Solution</u>''']] |
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| − | '''(a)'''
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| − | !Step 1:
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| − | !Step 2:
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| − | '''(b)'''
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| − | !Step 1:
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| − | !Step 2:
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| − | !Final Answer:
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| − | | '''(a)'''
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| − | | '''(b)'''
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| | [[009C_Sample_Final_3|'''<u>Return to Sample Exam</u>''']] | | [[009C_Sample_Final_3|'''<u>Return to Sample Exam</u>''']] |
Latest revision as of 18:39, 2 December 2017
Which of the following sequences 
converges? Which diverges? Give reasons for your answers!
(a) 
(b) 
Solution
Detailed Solution
Return to Sample Exam