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Maths-

General

Easy

Question

$Lt subscript x not stretchy rightwards arrow 3 end subscript fraction numerator x cubed minus 8 x squared plus 45 over denominator 2 x squared minus 3 x minus 9 end fraction$

$\frac{7}{3}$
$\frac{- 7}{3}$
$\frac{1}{3}$
$\frac{- 1}{3}$

hint Hint:

In the question we will first use the L hospital theorem. Then we can put the value of x in the question to get the answer.

The correct answer is: $fraction numerator negative 7 over denominator 3 end fraction$

$Lt subscript x not stretchy rightwards arrow 3 end subscript fraction numerator x cubed minus 8 x squared plus 45 over denominator 2 x squared minus 3 x minus 9 end fraction$
using L hospital theorem,
$limit as x rightwards arrow 3 of fraction numerator begin display style fraction numerator d x cubed minus 8 x squared plus 45 over denominator d x end fraction end style over denominator begin display style fraction numerator d 2 x squared minus 3 x minus 9 over denominator d x end fraction end style end fraction equals limit as x rightwards arrow 3 of fraction numerator 3 x squared minus 16 x over denominator 4 x minus 3 end fraction equals fraction numerator 3 cross times 9 minus 16 cross times 3 over denominator 4 cross times 3 minus 3 end fraction equals fraction numerator 27 minus 48 over denominator 12 minus 3 end fraction equals fraction numerator negative 21 over denominator 9 end fraction equals fraction numerator negative 7 over denominator 3 end fraction$

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