If Gx-25-x2 then lim x - 1Gx-G1-x-1 has the value

The correct option is D x→ 1lim √(25 x^2) ( √(24))/x 1 = x→ 1lim√(24) √(25 x^2)/x 1×√(24)+√(25 x^2)/√(24)+√(25 x^2) x→ 1limx^2 1/(x 1)[√(24)+√(25 x^2)] = 2/2√( ...

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Byju's Answer

Standard XI

Mathematics

Factorization Method Form to Remove Indeterminate Form

If Gx=-√25-x2...

Question

If G(x) = - $\sqrt{25 - x^{2}}$ then $lim x \to 1 \frac{G (x) - G (1)}{x - 1}$ has the value

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Solution

The correct option is D
$lim x \to 1 \frac{- \sqrt{25 - x^{2}} - (- \sqrt{24})}{x - 1}$
$= lim x \to 1 \frac{\sqrt{24} - \sqrt{25 - x^{2}}}{x - 1} \times \frac{\sqrt{24} + \sqrt{25 - x^{2}}}{\sqrt{24} + \sqrt{25 - x^{2}}}$
$lim x \to 1 \frac{x^{2} - 1}{(x - 1) [\sqrt{24} + \sqrt{25 - x^{2}}]} = \frac{2}{2 \sqrt{24}} = \frac{1}{2 \sqrt{6}}$

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Similar questions

Q. If

G (x) = - \sqrt{25 - x^{2}}

, then

lim x \to 1 \frac{G (x) - G (1)}{x - 1}

Q. If

G (x) = - \sqrt{25 - x^{2}}

, then

lim x \to 1 \frac{G (x) - G (1)}{x - 1} = \frac{1}{\sqrt{c}}

Find

c

Q. If

G (x) = \sqrt{25 - x^{2}}

, then what is

lim x \to 1 \frac{G (x) - G (1)}{x - 1}

equal to?

Q. If G(x) = -

\sqrt{25 - x^{2}}

then

lim x \to 1 \frac{G (x) - G (1)}{x - 1}

has the value

Q. If

g (x) = - \sqrt{25 - x^{2}}

, find

L t_{x \to 1} \frac{g (x) - g (1)}{x - 1}

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If G(x) = - √25−x2 then limx→1G(x)−G(1)x−1 has the value

The correct option is D limx→1−√25−x2−(−√24)x−1 =limx→1√24−√25−x2x−1×√24+√25−x2√24+√25−x2 limx→1x2−1(x−1)[√24+√25−x2]=22√24=12√6

If G(x) = - $\sqrt{25 - x^{2}}$ then $lim x \to 1 \frac{G (x) - G (1)}{x - 1}$ has the value