Evaluate the limit: (15(cos^2)x)/(7-7sinx)=? Help!?

Question

Evaluate the limit: (15(cos^2)x)/(7-7sinx)=?
This is as x goes to pi/2
Any help/adivce is greatly appreciated! :)

Answer 1

You can reduce this problem.

Multiply the top and the bottom by (1 + sinx)

On the top you'll get 15cos^2(x)(1 + sinx)

On the bottom, you'll get (7 - 7 sin^2(x))

divide out that 7, and you get:

7 * (1 - sin^2(x))

This is a trig identity. It turns into:

7 * cos^2(x)

now you have a cos^2(x) on the top and on the bottom.

They cancel.

Now you have:

15(1 + sinx) / 7

sin (pi / 2) = 1

15 ( 1 + 1 ) / 7 = 30 / 7

The reason this simplification works is because:

sin^2 + cos^2 = 1

This is an important trig identity -- remember it.

Answer 2

lim (x->π/2) 15 cos^2 x / (7 - 7 sin x)
= lim (x->π/2) 15 (1 - sin^2 x) / (7 (1 - sin x))
= lim (x->π/2) 15 (1 - sin x) (1 + sin x) / (7 (1 - sin x))
= lim (x->π/2) 15 (1 + sin x) / 7
= 15 (2) / 7
= 30/7.