calc help! L'Hospital's......?

Question

Evaluate the limit using L'Hopital's rule.

a) lim(as x--->0) of [7^(x)-14^(x)] / x
Evaluate the limit using L'Hopital's rule twice!
ans=______?

b) lim(as x--->0) of ( e^(9x)-1-9x) / (-9x^2)
Evaluate the limit using L'Hopital's rule if necessary
ans=______?

c) lim(as x--->1) of (7x+9) / (14x-9)
ans=______?

Answer 1

For a, I don't understand why it's twice. After one application you should be nicely done.

For b, numerator and denominator both go to 0, so it's necessary. In fact, it's necessary to do it twice, because the first derivatives of the numerator and denominator both go to 0 as x goes to 0.

c is really easy. Just evaluate the function at 1. (The answer is 16/5).