Question

Hi everyone,

Can someone please explain how Limit(1+cos(x))^tan(x) as x-> (pi/2) is equal to natural e?

My answer is 1, am I missing something here?

Answer 1

Let y = (1+cos(x))^tan(x)
Take the natural logarithm on both sides.
Write tanx as 1/(cos(x)/sin(x)
Take the limit as x->pi/2. You will notice you get a 0/0 form.
Apply L'Hospital's rule and differentiate top and bottom, simplify.

Answer 2

You will find the limit of ln(y) as x->pi/2 is 1
That means limit y as x->pi/2 is e.

Answer 3

ohhhhhhhhhhh

Answer 4

i think i understand now thanks so much!

Answer 5

you are welcome.