Maths-
General
Easy

Question

Lt subscript x not stretchy rightwards arrow straight infinity end subscript open parentheses square root of x squared plus x end root minus x close parentheses

  1. 1
  2. -1
  3. 0
  4. 1 half

hintHint:

In this question first we will rationalize the equation then we will divide the equation by x and then put the value of x.

The correct answer is: 1 half


    space space space space Lt subscript x not stretchy rightwards arrow straight infinity end subscript open parentheses square root of x squared plus x end root minus x close parentheses
equals space Lt subscript x not stretchy rightwards arrow straight infinity end subscript open parentheses square root of x squared plus x end root minus x close parentheses cross times fraction numerator square root of x squared plus x end root plus x over denominator square root of x squared plus x end root plus x end fraction
equals Lt subscript x not stretchy rightwards arrow straight infinity end subscript fraction numerator x squared plus x minus x squared over denominator square root of x squared plus x end root plus x end fraction
equals Lt subscript x not stretchy rightwards arrow straight infinity end subscript fraction numerator x over denominator square root of x squared plus x end root plus x end fraction
D i v i d i n g space b y space x comma space
equals Lt subscript x not stretchy rightwards arrow straight infinity end subscript fraction numerator 1 over denominator square root of 1 plus begin display style 1 over x end style end root plus 1 end fraction
equals fraction numerator 1 over denominator square root of 1 plus 1 end fraction
equals 1 half.

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