Higgins Santiago
01/21/2023 · High School
Use l'Hôpital's rule to find the following limit. \( \lim _{x \rightarrow \pi / 2^{-}}(-9 \sec x+9 \tan x) \)
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Step-by-step Solution
Calculate the limit \( \lim_{x\rightarrow \pi/2^{-}}(-9\sec x+9\tan x) \).
Evaluate the limit by following steps:
- step0: Evaluate the limit:
\(\lim _{x\rightarrow \left(\frac{\pi }{2}\right)^{-}}\left(-9\sec\left(x\right)+9\tan\left(x\right)\right)\)
- step1: Calculate:
\(\lim _{x\rightarrow \frac{\pi }{2}^{-}}\left(-9\sec\left(x\right)+9\tan\left(x\right)\right)\)
- step2: Transform the expression:
\(\lim _{x\rightarrow \frac{\pi }{2}^{-}}\left(-\frac{9}{\sec\left(x\right)+\tan\left(x\right)}\right)\)
- step3: Rewrite the expression:
\(-\lim _{x\rightarrow \frac{\pi }{2}^{-}}\left(\frac{9}{\sec\left(x\right)+\tan\left(x\right)}\right)\)
- step4: Calculate:
\(0\)
Using l'Hôpital's rule, we find that the limit \( \lim _{x \rightarrow \pi / 2^{-}}(-9 \sec x+9 \tan x) \) is equal to 0.
Quick Answer
The limit is 0.
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