Question

lim_{x rightarrow 1}sqrt{x+3}-2over lim_{x rightarrow 1}sqrt{10-x}-3

Answer 1

\[\lim_{x \rightarrow 1}\sqrt{x+3}-2\over \lim_{x \rightarrow 1}\sqrt{10-x}-3\]

Answer 2

0
\or 0/0

Answer 3

no thats not the answer

Answer 4

-1 final answer

Answer 5

how do you get that?

Answer 6

when you initially evaluate a lim and get an indeterminate answer such as 0/0
use L'hopitals rule which says an equivalent limit can be obtained by differentiating the top and bottom then re-evaluating
After differentiating:
\[\lim_{x \rightarrow 1} \frac{\frac{1}{2\sqrt{x+3}}}{-\frac{1}{2\sqrt{10-x}}} = \lim_{x \rightarrow 1} -\frac{\sqrt{10-x}}{\sqrt{x+3}} = -\frac{3}{2}\]