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

Find the limits
$\underset{x\to 0}{lim}\mathrm{sec}\left[{e}^{x}+\pi \mathrm{tan}\left(\frac{\pi }{4\mathrm{sec}x}\right)-1\right]$
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Given
The given expression is $\underset{x\to 0}{lim}\mathrm{sec}\left[{e}^{x}+\pi \mathrm{tan}\left(\frac{\pi }{4\mathrm{sec}x}\right)-1\right]$
find the limit
$\underset{x\to 0}{lim}\mathrm{sec}\left[{e}^{x}+\pi \mathrm{tan}\left(\frac{\pi }{4\mathrm{sec}x}\right)-1\right]=\mathrm{sec}\left[{e}^{0}+\pi \mathrm{tan}\left(\frac{\pi }{4\mathrm{sec}\left(0\right)}\right)-1\right]$
$=\mathrm{sec}\left[1+\pi \mathrm{tan}\left(\frac{\pi }{4}\right)-1\right]$
$=\mathrm{sec}\left(\pi \right)$
$=-1$