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  • Please help! - Limit , continuity and differentiability - JEE Main-6

\lim_{x\rightarrow 5}\frac{\sqrt{4x+5}-\sqrt{6x-5}}{x-5} equals

  • Option 1)

    0

  • Option 2)

    -1/5

  • Option 3)

    -2/5

  • Option 4)

    -3/5

 

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 5}\frac{\sqrt{4x+5}-\sqrt{6x-5}}{x-5}\times \frac{\sqrt{4x+5}+\sqrt{6x-5}}{\sqrt{4x+5}+\sqrt{6x-5}}

\lim_{x\rightarrow 5}\frac{-2(x-5)}{(x-5)(\sqrt{4x+5}+\sqrt{6x-5})}

\lim_{x\rightarrow 5}\frac{-2}{(\sqrt{4x+5}+\sqrt{6x-5})}=-2/10=-1/5

 

 

 

 


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Posted by

Himanshu

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