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Maths-

General

Easy

Question

$text Lt end text subscript x not stretchy rightwards arrow straight infinity end subscript left parenthesis square root of x plus 1 end root minus square root of x right parenthesis$

1
-1
0
Infty

hint Hint:

In this question, we have to find the value for that first we will rationalize and then use the L' Hospital theorem and later put the value of x.

The correct answer is: 0

$text Lt end text subscript x not stretchy rightwards arrow straight infinity end subscript left parenthesis square root of x plus 1 end root minus square root of x right parenthesis equals text Lt end text subscript x not stretchy rightwards arrow straight infinity end subscript left parenthesis square root of x plus 1 end root minus square root of x right parenthesis cross times fraction numerator left parenthesis square root of x plus 1 end root plus square root of x right parenthesis over denominator left parenthesis square root of x plus 1 end root plus square root of x right parenthesis end fraction equals straight c fraction numerator x plus 1 minus x over denominator left parenthesis square root of x plus 1 end root plus square root of x right parenthesis end fraction text = Lt end text subscript x not stretchy rightwards arrow straight infinity end subscript fraction numerator 1 over denominator square root of x open parentheses square root of 1 plus begin display style 1 over x end style end root text +1 end text close parentheses end fraction equals space 1 over infinity cross times fraction numerator 1 over denominator square root of 1 plus begin display style 1 over infinity end style end root plus 1 end fraction equals 0 cross times 1 over 1 equals 0.$

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