Math  /  Calculus

QuestionCompute the following limits using L'Hospital's rule if appropriate. Use INF to denote oo and MINF to denote limx177x21=limxtan1(x)(1/x)7=\begin{array}{l} \lim _{x \rightarrow 1} \frac{7^{\infty}-7}{x^{2}-1}=\square \\ \lim _{x \rightarrow \infty} \frac{\tan ^{-1}(x)}{(1 / x)-7}= \end{array} \square
Note: You can earn partial credit on this problem.

Studdy Solution
Determine if L'Hospital's Rule is applicable:
The limit limxtan1(x)(1/x)7\lim _{x \rightarrow \infty} \frac{\tan ^{-1}(x)}{(1 / x)-7} results in π27\frac{\frac{\pi}{2}}{-7}, which is not an indeterminate form.
Therefore, the limit is π14-\frac{\pi}{14}.
The solutions to the limits are:
1. limx177x21=INF\lim _{x \rightarrow 1} \frac{7^{\infty}-7}{x^{2}-1} = \text{INF}
2. limxtan1(x)(1/x)7=π14\lim _{x \rightarrow \infty} \frac{\tan ^{-1}(x)}{(1 / x)-7} = -\frac{\pi}{14}

View Full Solution - Free
Was this helpful?

Studdy solves anything!

banner

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

ParentsInfluencer programContactPolicyTerms
TwitterInstagramFacebookTikTokDiscord