Question

I need some help with limits.

Answer 1

1. Try direct substitution
2. If direct substitution gives you an indeterminate solution, such as 0/0 or inf/inf, try L'Hopital's Rule.

Answer 2

What is L'Hopital's Rule?

Answer 3

Idr the exact definition, but if direct substitution doesn't work for finding a limit, this rule can solve it.
Take the derivative of the numerator, keep it there. Take the derivative of the denominator, keep it there. Plug in your limit value again.
If still indeterminate, apply the rule again.
If it doesn't work, you'll have to try a different method.

Answer 4

I found this https://www.khanacademy.org/math/differential-calculus/derivative_applications/lhopital_rule/v/introduction-to-l-hopital-s-rule

Answer 5

\[\begin{align*}\lim_{x\to5}\frac{\sqrt{x^2+11}-6}{x-5}\times\frac{\sqrt{x^2+11}+6}{\sqrt{x^2+11}+6}&=\lim_{x\to5}\frac{x^2+11-36}{(x-5)(\sqrt{x^2+11}+6)}\\\\
&=\lim_{x\to5}\frac{x^2-25}{(x-5)(\sqrt{x^2+11}+6)}
\end{align*}\]

Answer 6

where siths left just cancel (x-5) top and bottom
top you have (x^2-25)=(x-5)(x+5)

Answer 7

Ah ok, I see