Mathematics

Problem

Define the composite function

p

p(x)=\mathrm{e}^{\tan(x)}

for all

x

in the open interval

\left(-\dfrac{\pi}{2},\dfrac{\pi}{2}\right)

. (a) Evaluate

\displaystyle\lim_{x\to 0}p(x)

. (b) Verify that

p

is continuous at

x=0

by checking each requirement of the formal definition. (c) For

x=\dfrac{\pi}{4}

, calculate

p\!\left(\dfrac{\pi}{4}\right)

and interpret its meaning in terms of the inner and outer functions that compose

p