MyQuestionIcon

1

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Theorems for Continuity

Solve: lim ...

Question

Solve:
${lim}_{x \to 2} \frac{\sqrt{x^{3} - 4} - 2}{\sqrt{20 - x^{2}} - 4}$

Open in App

Solution

${lim}_{x \to 2} \frac{\sqrt{x^{3} - 4} - 2}{\sqrt{20 - x^{2}} - 4} = \frac{0}{0}$ form
Applying L' Hospital's rule
$= \frac{\frac{1}{2 \sqrt{x^{3} - 4}} (3 x^{2})}{\frac{1}{2 \sqrt{20 - x^{2}}} (- 2 x)} = {lim}_{x \to 2} \frac{\sqrt{20 - x^{2}}}{\sqrt{x^{3} - 4}} (\frac{- 3}{2} x) = \frac{\sqrt{20 - 4}}{\sqrt{8 - 4}} \times \frac{- 3}{2} \times 2 = \frac{4}{2} \times - 3 = - 6$

Suggest Corrections

thumbs-up

0

Similar questions

lim x \to 4 \frac{x^{3} - 64}{x^{2} - 16}

Q. Find the limits :

i .

lim x \to 1 [\frac{x^{2} + 1}{x + 100}]

i i .

lim x \to 2 [\frac{x^{3} - 4 x^{2} + 4 x}{x^{2} - 4}]

i i i .

lim x \to 2 [\frac{x^{2} - 4}{x^{3} - 4 x^{2} + 4 x}]

i v .

lim x \to 2 [\frac{x^{3} - 2 x^{2}}{x^{2} - 5 x + 6}]

v .

lim x \to 1 [\frac{x - 2}{x^{2} - x} - \frac{1}{x^{3} - 3 x^{2} + 2 x}]

lim x \to 2 \frac{x^{3} - 8}{x^{2} - 4}

lim x \to 2 \frac{x^{2} - 5 x + 6}{x^{2} - 4}

lim x \to - 4 \frac{x + 4}{x^{2} - x - 20}

View More

Join BYJU'S Learning Program

similar_icon

Related Videos

lock

Algebra of Continuous Functions

MATHEMATICS

Watch in App

explore_more_icon

Explore more

Theorems for Continuity

Standard XII Mathematics

Join BYJU'S Learning Program

CrossIcon