Find the limits lim_{xrightarrow0}sec[e^x+pitan(frac{pi}{4sec x})-1]

Question
Limits and continuity
asked 2021-02-21
Find the limits
\(\lim_{x\rightarrow0}\sec[e^x+\pi\tan(\frac{\pi}{4\sec x})-1]\)

Answers (1)

2021-02-22
Given
The given expression is \(\lim_{x\rightarrow0}\sec[e^x+\pi\tan(\frac{\pi}{4\sec x})-1]\)
find the limit
\(\lim_{x\rightarrow0}\sec[e^x+\pi\tan(\frac{\pi}{4\sec x})-1]=\sec[e^0+\pi\tan(\frac{\pi}{4\sec(0)})-1]\)
\(=\sec[1+\pi\tan(\frac{\pi}{4})-1]\)
\(=\sec(\pi)\)
\(=-1\)
0

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