Maths-
General
Easy

Question

L t subscript x not stretchy rightwards arrow 0 end subscript fraction numerator x over denominator square root of x plus 4 end root minus 2 end fraction equals

  1. 4
  2. 2 square root of 2
  3. fraction numerator 1 over denominator square root of 2 end fraction
  4. square root of 2

Hint:

In the question we will use L hospital theorem, fraction numerator f left parenthesis x right parenthesis over denominator g left parenthesis x right parenthesis end fraction equals fraction numerator f apostrophe left parenthesis x right parenthesis over denominator g apostrophe left parenthesis x right parenthesis end fraction.

The correct answer is: 4


    L t subscript x not stretchy rightwards arrow 0 end subscript fraction numerator x over denominator square root of x plus 4 end root minus 2 end fraction
u sin g space L h o s p i t a l space t h e o r e m comma space
equals L t subscript x not stretchy rightwards arrow 0 end subscript fraction numerator begin display style fraction numerator d blank over denominator d x end fraction end style x over denominator begin display style fraction numerator d blank over denominator d x end fraction end style square root of x plus 4 end root minus 2 end fraction
equals L t subscript x not stretchy rightwards arrow 0 end subscript fraction numerator 1 over denominator begin display style fraction numerator 1 over denominator 2 square root of x plus 4 end root end fraction end style end fraction
equals L t subscript x not stretchy rightwards arrow 0 end subscript 2 square root of x plus 4 end root
equals 2 square root of 0 plus 4 end root
equals 2 cross times 2
equals 4

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