Question

lim a->36 (36-a)/6-sqrt(a)

Answer 1

\[\lim_{a \rightarrow 36}\frac{36-a}{6-\sqrt{a}}\]If you plug in 36, you get 0/0, which is an indeterminate form, which means you get to use L'hospital's rule, which means you take the derivative of both the numerator and denominator and then try to take the limit again.\[\lim_{a \rightarrow 36}\frac{-1}{-\frac{1}{2\sqrt{a}}}=\lim_{a \rightarrow 36}2\sqrt{a}=2\sqrt{36}=12\]

Answer 2

If you don't know L'Hopital's rule yet, multiply the numerator and denominator by the denominator's conjugate:
\[\lim_{a\to36}\frac{36-a}{6-\sqrt a}\cdot\frac{6+\sqrt a}{6+\sqrt a}=\lim_{a\to36}\frac{(36-a)(6+\sqrt a)}{36-a}=\lim_{a\to36}(6+\sqrt a)\]

Answer 3

none of these are correct. sorry guys, i tried submitting both answers online but to no avail.

Answer 4

This is proof that it's 12: http://www.wolframalpha.com/input/?i=lim+a-%3E36+%2836-a%29%2F%286-sqrt%28a%29%29
However, it's possible that you meant the equation below.\[\lim_{a \rightarrow 36} (\frac{36-a}{6}-\sqrt{a})=0-\sqrt{36}=-6\]

Answer 5

nvm, sorry about the confusion. Thanks!