Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa

\lim_{x\rightarrow 4}\frac{\sqrt{x+5}-3}{x-4} equals

Option: 1

1/3


Option: 2

1/4


Option: 3

1/5


Option: 4

1/6


Answers (1)

best_answer

As we have learned

Method of Rationalisation -

Rationalisation method is used when we have RADICAL SIGNS in an expression.(like  1/2,  1/3 etc) and there exists a negative sign between two terms of an algebraic expression.

- wherein

\lim_{x\rightarrow a}\:\frac{x-a}{\sqrt{x}-\sqrt{a}}


\therefore \:\frac{(x-a)(\sqrt{x}+\sqrt{a})}{(\sqrt{x}-\sqrt{a})(\sqrt{x}+\sqrt{a})}


=\sqrt{x}+\sqrt{a}

=\sqrt{a}+\sqrt{a}

=2\sqrt{a}

 

 \lim_{x\rightarrow 4}\frac{\sqrt{x+5}-3}{x-4}\times \frac{\sqrt{x+5}+3}{\sqrt{x+5}+3}= \lim_{x\rightarrow 4}\frac{(x-4)}{(x-4)(\sqrt{x+5}+3)}

\lim_{x\rightarrow 4}\frac{1}{\sqrt{x+5}+3}= \frac{1}{3+3}= 1/6

 

 

Posted by

SANGALDEEP SINGH

View full answer

Similar Questions