Question

How to solve the limit?

How to solve the limit
lim e^tg(x)
x→(π/2)+ (by the right)

Answer 1

`lim_(x->(pi/2)^+) e^tanx = 0`

Explanation:

Substitute `y= tanx`

`lim_(x->(pi/2)^+) tanx = -oo`

so:

`lim_(x->(pi/2)^+) e^tanx = lim_(y->-oo) e^y = 0`

graph{e^tanx [-1, 3, -1, 10]}