Sayeth What?

Calculus Level 3

$\lim _{ x\rightarrow 0 }{ \left ( \ \sqrt { \frac { 1 }{ { x }^{ 2 } } +\frac { 1 }{ x } } -\sqrt { \frac { 1 }{ { x }^{ 2 } } -\frac { 1 }{ x } } \ \right ) } = \ ?$

-1

1

0

Does not exist None of these choices

1 solution

Ramesh Goenka
Mar 19, 2015

It should be 1. LHL=RHL=1

Deepak Kumar - 6 years, 2 months ago

Yes it should be 1.I also got the answer as 1

Vishal S - 6 years, 1 month ago

u r making same silly mistake.see my other comment .And the same mistake is there in the solution here.

Deepak Kumar - 6 years, 1 month ago

Helpful graph . (When solving, I accidentally assumed that $\sqrt{\frac1{x^2}}=\frac1x$ , and factored it out... it's actually equal to $\lvert\frac1x\rvert$ .)

Akiva Weinberger - 6 years, 1 month ago

Yup made the same silly mistake :) (x^2)^1/2=|x|

Deepak Kumar - 6 years, 1 month ago

Sayeth What?

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