Maths-
General
Easy

Question

Lt subscript x not stretchy rightwards arrow 1 end subscript space fraction numerator x minus 1 over denominator 2 x squared minus 7 x plus 5 end fraction

  1. 1 third
  2. 3
  3. fraction numerator negative 1 over denominator 3 end fraction
  4. -3

Hint:

In the question we will first use the 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 open parentheses x close parentheses end fraction. Then we will put the value of x to get the answer.

The correct answer is: fraction numerator negative 1 over denominator 3 end fraction


    Lt subscript x not stretchy rightwards arrow 1 end subscript space fraction numerator x minus 1 over denominator 2 x squared minus 7 x plus 5 end fraction
    using L hospital theorem,
    equals limit as x rightwards arrow 1 of fraction numerator begin display style fraction numerator d x minus 1 over denominator d x end fraction end style over denominator begin display style fraction numerator d 2 x squared minus 7 x plus 5 over denominator d x end fraction end style end fraction
equals limit as x rightwards arrow 1 of fraction numerator 1 over denominator 4 x minus 7 end fraction
equals fraction numerator 1 over denominator 4 cross times 1 minus 7 end fraction
equals fraction numerator negative 1 over denominator 3 end fraction

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