Question

$\text{The value of}\underset{x\to 0}{lim}\frac{\underset{0}{\overset{x^2}{\int }}cos{t}^{2}dt}{xsinx}\text{is}$

• A. 3/2
• B. 1
• C. -1
• D. 2

Answer 1

The correct option is B

1

$\underset{x\to 0}{lim}\frac{\underset{0}{\overset{x^2}{\int }}cos{t}^{2}dt}{xsinx}\left(\frac{0}{0}form\right)=\underset{x\to 0}{lim}\frac{2xcos{x}^4}{xcosx+sinx}\text{[Using L'Hospital's Rule]}=\underset{x\to 0}{lim}\frac{2cos{x}^4-8x^{4}sin{x}^4}{2cosx-sinx}\text{[Using L'Hospital's Rule again]}=\frac{2-0}{2-0}=1$