Question

Find the limit as x approaches 4.

[sqrt(x^2-1)-sqrt(15)]/(x-4)

Answer 1

I drew it to clarify

Answer 2

Lhopital rule. Derivative of top and bottom.

Answer 3

Could you show me how to find the derivative?

Answer 4

(1/2)(x^2 - 1)^(-1/2) * 2x

Answer 5

chain rule for the first one

Answer 6

bottom basically turns to 1 because you have the variable to the first power and plus or minus a constant

Answer 7

The top should be rewritten to (x^2 - 1)^(1/2) - (15)^(1/2)
The constant(15^1/2) turns into a zero.
So you're left only doing (x^2 - 1)^(1/2).
Drop the power so you get (1/2)(x^2 -1 )^(-1/2)
Then you do chain rule. Derive the inside you end up getting (x)(x^2 -1)^(-1/2)