Question

$\underset{x\to 0}{lim}\frac{d}{dx}\int \frac{1-cosx}{x^2}dx$ is equal to ?

• A. $\frac{1}{2}$
• B. $-\frac{1}{2}$
• C. $0$
• D. $1$

Answer 1

Answer: (A)

$\frac{1}{2}$

$\underset{x\to 0}{lim}\frac{d}{dx}\int \frac{1-cosx}{x^2}dx=\underset{x\to 0}{lim}\frac{1-cosx}{x^2}$

$=\underset{x\to 0}{lim}\frac{1-cosx}{x^2}=\underset{x\to 0}{lim}\frac{2{\sin }^2\frac{x}{2}}{x^2}$

$=\frac{1}{2}\underset{x\to 0}{lim}{\left(\frac{\sin \frac{x}{2}}{\frac{x}{2}}\right)}^2=\frac{1}{2}$