\lim_{x\toa} {(\sqrt{3x-a}-\sqrt{(x+a)})}/{(x-a)}=

AP ICET 2017 Shift 1 Paper

Question : 134 of 200

Marks: +1, -0

\lim↙{x→a}\;\;{(√{3x-a}-√{(x+a)})}/{(x-a)}=

Solution:

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

For x = a it is of

0/0

form. We can apply L’ Hospital rule.

=\lim↙{x→a}{\;\;{3}/{2√{3x-a}}-{1}/{2√{x+a}}}/{(1-0)}

=\lim↙{x→a}{3}/{2√{3x-a}}-\;\;{1}/{2√{x+a}}

={1}/{2}[{3}/{√{2a}}-{1}/{√{2a}}]={1}/{2}×{2}/{√{2a}}={1}/{√{2a}}

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