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Maths-

General

Easy

Question

$L t left parenthesis x rightwards arrow d right parenthesis left parenthesis left parenthesis 2 vertical line x vertical line right parenthesis divided by x plus x plus 1 right parenthesis$

3
1
2
0

hint Hint:

We are given a function. We have to find the limit.

The correct answer is: 3

The given function is $f open parentheses x close parentheses equals fraction numerator 2 vertical line x vertical line over denominator x end fraction plus x plus 1$
We have to find the limit of the function.
$limit as x rightwards arrow 0 to the power of plus of f open parentheses x close parentheses equals limit as x rightwards arrow 0 to the power of plus of fraction numerator 2 vertical line x vertical line over denominator x end fraction plus x plus 1$
|x| can have two values, positive and negative.
|x| = x x>0
|x| = -x x<0
In this care the limit is right hand limit tending to zero.
So, x>0
|x| = x
$limit as x rightwards arrow 0 of f open parentheses x close parentheses equals limit as x rightwards arrow 0 to the power of plus of fraction numerator 2 vertical line x vertical line over denominator x end fraction plus x plus 1 space space space space space space space space space space space space space space equals limit as x rightwards arrow 0 to the power of plus of fraction numerator 2 x over denominator x end fraction plus x space plus space 1 space space space space space space space space space space space space space space equals limit as x rightwards arrow 0 to the power of plus of 2 space plus space x space plus space 1 space space space space space space space space space space space space space space equals space 2 space plus space 0 space plus space 1 space space space space space space space space space space space space space space space equals space 3$
The final value is 3.

For such questions, we should know different formulas of limit.

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