\lim_{x\to3} {x-3}/\sqrt{x-2} -\sqrt{4-x}

TS ICET 2015 Question Paper with Solutions for online practice

Question : 140 of 200

Marks: +1, -0

\lim ↙{x→3}

{x-3}/{√{x-2} -√{4-x}}

Solution:

\lim↙{x→3}{x-3}/{√{x-2}-√{4-x}}

=\lim↙{x→3}{(x-3)(√{x-2}+√{4-x})}/{(√{x-2})^{2}-(√{4-x})^{2}}

=\lim↙{x→3}{(x-3)(√{x-2}+√{4-x})}/{(x-2)-(4-x)}

=\lim↙{x→3}{(x-3)(√{x-2}+√{4-x})}/{2(x-3)}

=\lim↙{x→3}{√{x-2}+√{4-x}}/{2}={√{3-2}+√{4-3}}/{2}

={1+1}/{2}=1

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