Maths-
General
Easy

Question

Lt subscript x not stretchy rightwards arrow 3 end subscript fraction numerator 4 x squared minus 17 x plus 15 over denominator x squared minus x minus 6 end fraction

  1. 1 fifth
  2. fraction numerator negative 1 over denominator 5 end fraction
  3. 7 over 5
  4. fraction numerator negative 7 over denominator 5 end fraction

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: 7 over 5


    Lt subscript x not stretchy rightwards arrow 3 end subscript fraction numerator 4 x squared minus 17 x plus 15 over denominator x squared minus x minus 6 end fraction
    using L hospital theorem,
    limit as x rightwards arrow 3 of fraction numerator begin display style fraction numerator d 4 x squared minus 17 x plus 15 over denominator d x end fraction end style over denominator begin display style fraction numerator d x squared minus x minus 6 over denominator d x end fraction end style end fraction
equals limit as x rightwards arrow 3 of fraction numerator 8 x minus 17 over denominator 2 x minus 1 end fraction
equals fraction numerator 8 cross times 3 minus 17 over denominator 2 cross times 3 minus 1 end fraction
equals fraction numerator 24 minus 17 over denominator 6 minus 1 end fraction
equals 7 over 5

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