Question

Question #3ade9

Answer 1

`-2`

Explanation:

I edited your question a bit, and I hope that this is the limit you are looking for.

By lH`hat"o"`pital's Rule,

`lim_(theta to pi/2)(2theta-pi)/(cos theta)=lim_(theta to pi/2)2/-sin theta=2/(-sin(pi/2))=2/(-1)=-2`

I hope that this was clear.

Answer 2

`-2.`

Explanation:

Without using L'Hospital's Rule, the Limit can be derived as

shown below:

Let, `theta=x+pi/2. :. theta to pi/2 rArr x to 0.`

`:." The Reqd. Lim.="lim_(x to 0){2(x+pi/2)-pi}/cos(x+pi/2),`

`=lim_(x to 0) (2x)/(-sinx)=(-2){lim_(x to 0)x/sinx}.`

`:." The Reqd. Lim."=-2.`

Enjoy Maths.!