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Maths-

General

Easy

Question

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

$\frac{1}{3}$
3
$\frac{- 1}{3}$
-3

hint 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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