MyQuestionIcon

1

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

Differentiation of Inverse Trigonometric Functions

Solve lim x...

Question

Solve ${lim}_{x \to 0} \frac{\sqrt{1 + sin x} - \sqrt{1 - sin x}}{x}$

Open in App

Solution

${lim}_{x \to 0} \frac{\sqrt{1 + sin x} - \sqrt{1 - sin x}}{x}$
This is $\frac{0}{0}$ form so by using L hospital rule
${lim}_{x \to 0} \frac{- \frac{c o s x}{\sqrt{1 + sin x}} - \frac{c o s x}{\sqrt{1 - sin x}}}{1} = - 2$

Suggest Corrections

thumbs-up

1

Similar questions

lim x \to 0 \frac{\sqrt{1 + sin x} - \sqrt{1 - sin x}}{x}

lim x \to 0 \frac{\sqrt{1 + sin x} - \sqrt{1 - sin x}}{x}

{lim}_{x \to 0} \frac{\sqrt[3]{1 + s i n x} - \sqrt[3]{1 - s i n x}}{x}

lim x \to - 1 \frac{x^{2} - x - 2}{(x^{2} + x) + sin (x + 1)}

Q. Evaluate the following limit:

lim x \to 0 \frac{\sqrt{(1 + sin x)} - \sqrt{(1 - sin x)}}{x}

View More

Join BYJU'S Learning Program

similar_icon

Related Videos

lock

Differentiating Inverse Trignometric Function

MATHEMATICS

Watch in App

explore_more_icon

Explore more

Differentiation of Inverse Trigonometric Functions

Standard XII Mathematics

Join BYJU'S Learning Program

CrossIcon