Given

The given expression is \(\lim_{x\rightarrow0}\sec[e^x+\pi\tan(\frac{\pi}{4\sec x})-1]\)

find the limit

\(\lim_{x\rightarrow0}\sec[e^x+\pi\tan(\frac{\pi}{4\sec x})-1]=\sec[e^0+\pi\tan(\frac{\pi}{4\sec(0)})-1]\)

\(=\sec[1+\pi\tan(\frac{\pi}{4})-1]\)

\(=\sec(\pi)\)

\(=-1\)

The given expression is \(\lim_{x\rightarrow0}\sec[e^x+\pi\tan(\frac{\pi}{4\sec x})-1]\)

find the limit

\(\lim_{x\rightarrow0}\sec[e^x+\pi\tan(\frac{\pi}{4\sec x})-1]=\sec[e^0+\pi\tan(\frac{\pi}{4\sec(0)})-1]\)

\(=\sec[1+\pi\tan(\frac{\pi}{4})-1]\)

\(=\sec(\pi)\)

\(=-1\)