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Question

L t subscript x not stretchy rightwards arrow 0 end subscript fraction numerator square root of x plus 1 end root minus 1 over denominator x end fraction

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

Hint:

To find the limit of the equation we will first write x+1 =y then we will convert limit of x to limit of y then we will rationalize the equation after which we will put the value of y.

The correct answer is: 1 half


    L t subscript x not stretchy rightwards arrow 0 end subscript fraction numerator square root of x plus 1 end root minus 1 over denominator x end fraction
    L e t space left parenthesis x plus 1 right parenthesis equals y
A s space x rightwards arrow 0
space space space space y rightwards arrow 1 plus 0
space space space space space y rightwards arrow 1
rightwards double arrow limit as y rightwards arrow 1 of fraction numerator square root of y minus 1 over denominator y minus 1 end fraction
rightwards double arrow limit as y rightwards arrow 1 of fraction numerator square root of y minus 1 over denominator open parentheses square root of y close parentheses squared minus 1 end fraction
rightwards double arrow limit as y rightwards arrow 1 of fraction numerator square root of y minus 1 over denominator left parenthesis square root of y minus 1 right parenthesis left parenthesis square root of y plus 1 right parenthesis end fraction
rightwards double arrow limit as y rightwards arrow 1 of fraction numerator 1 over denominator left parenthesis square root of y plus 1 right parenthesis end fraction
rightwards double arrow fraction numerator 1 over denominator square root of 1 plus 1 end fraction
rightwards double arrow 1 half
space space space space

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