Question

lim of x to 1 of (sqrt(2-x)-1)/(sqrt(5-x)-2)

Answer 1

youwant an answer? or steps?

Answer 2

stepsss

Answer 3

play with conjugates when dealing with sqrts
\[\lim_{x\ to\ 1} \frac{\sqrt{2-x}-1}{\sqrt{5-x}-2}\]

Answer 4

\[\lim_{x\ to\ 1} \frac{\sqrt{2-x}-1}{\sqrt{5-x}-2}*\frac{\sqrt{5-x}+2}{\sqrt{5-x}+2}\]
\[\lim_{x\ to\ 1} \frac{\sqrt{(2-x)(5-x)}-\sqrt{5-x}+2\sqrt{2-x}-2}{5-x-4}\]

Answer 5

\[\lim_{x\ to\ 1} \frac{\sqrt{(2-x)(5-x)}-\sqrt{5-x}+2\sqrt{2-x}-2}{1-x}\]

doesnt always work out nice but most of the time it does :)

Answer 6

what methods you allowed to use? LHopital?

Answer 7

no derivatives

Answer 8

:/

Answer 9

\[\lim_{x\rightarrow 1}\frac{\sqrt{2-x}-1}{\sqrt{5-x}-2}=
\lim_{y\rightarrow 0}\frac{\sqrt{1-y}-1}{\sqrt{4-y}-2}=\frac{1}{2}\,\lim_{y\rightarrow 0}\frac{\sqrt{1-y}-1}{\sqrt{1-y/4}-1}=\]
\[=\frac{1}{2}\,\lim_{y\rightarrow 0}\frac{1-y/2-1}{1-y/8-1}=\frac{1}{2}\cdot 4=2\]