Use l'Hospital's Rule. i cant find the answers please help me?

Question

find ( x ^ 2 – 25) / ( x + 5 )
x-- > - 5
and also

find lim ( x ) / ( tan ^ -1 ( 9x )
x----->0

Answer 1

#1: First take the derivative of the top and bottom of the function.
( 2*x ) / ( 1 ) = ( 2 *x)
Then see that the limit approaches -10 because (2 * -5 ) = -10

Answer 2

For the first you don´t need L´Hòpital as
x^2-25 = (x+5) ( x-5) so simplifying for x not -5
lim(x-5) for x=>-5 = -10
For the 2nd
= lim 1/[(1/(1+81x^2)] *9 which has lim =1/9