The value of lim x- 7 2- x-3 x 2 -49 is

The correct option is D 1 56 lim _ x→ 7 ( 2 √( x 3 ) #160; x ^ 2 49 #160;) #160; Applying L'Hospital's rule, =lim _ x→ 7 ( 0 1 2√ ...

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Standard XII

Mathematics

Rationalization Method to Remove Indeterminate Form

The value of ...

Question

The value of ${lim}_{x \to 7} (\frac{2 - \sqrt{x - 3}}{x^{2} - 49})$ is

\frac{2}{9}

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- \frac{2}{49}

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- \frac{1}{56}

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- \frac{1}{59}

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Solution

The correct option is D $- \frac{1}{56}$
${lim}_{x \to 7} (\frac{2 - \sqrt{x - 3}}{x^{2} - 49})$
Applying L'Hospital's rule,
$= {lim}_{x \to 7} ⎛ ⎜ ⎜ ⎜ ⎝ \frac{0 - \frac{1}{2 \sqrt{x - 3}}}{2 x} ⎞ ⎟ ⎟ ⎟ ⎠$
$= {lim}_{x \to 7} \frac{- 1}{4 x \sqrt{x - 3}}$
$= \frac{- 1}{4.7 \sqrt{7 - 3}} = - \frac{1}{56}$

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Similar questions

Let f(x) = $x^{2}$ -1, 0 0<x<2 and 2x+3, 2 $\leq$ x<3, The quadratic equation whose roots are ${lim}_{x \to 2^{-}} f (x), a n d {lim}_{x \to 2^{+}} f (x)$

$I f 3 x - 7 y = 10 a n d x y = - 1, f i n d t h e v a l u e o f 9 x^{2} + 49 y^{2}$

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, then the value of

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The value of limx→7(2−√x−3x2−49) is

The correct option is D −156limx→7(2−√x−3x2−49)Applying L'Hospital's rule,=limx→7⎛⎜ ⎜ ⎜⎝0−12√x−32x⎞⎟ ⎟ ⎟⎠=limx→7−14x√x−3=−14.7√7−3=−156

The value of ${lim}_{x \to 7} (\frac{2 - \sqrt{x - 3}}{x^{2} - 49})$ is