Question

The value of $\lim _ { x \rightarrow 0 }$ $\frac { \int _ { 0 } ^ { x } \cos t ^ { 2 } d t } { x }$ is –

• A. 1
• B. 0
• C. – 1
• D. 2

Answer 1

Answer: (A)

1

Answer 2

Let ƒ(x) = $\int _ { 0 } ^ { \mathrm { x } } \cos ^ { 2 } \mathrm { dt }$ and g(x) = x. Then ƒ(0) = g(0) = 0.

\ $\lim _ { x \rightarrow 0 }$ = $\lim _ { x \rightarrow 0 }$

Ž $\lim _ { x \rightarrow 0 }$ $\frac { \int _ { 0 } ^ { x } \cos t ^ { 2 } d t } { x }$ = $\lim _ { x \rightarrow 0 }$ $\frac { \cos x ^ { 2 } .1 - \cos 0.0 } { 1 }$

= $\lim _ { x \rightarrow 0 }$ $\frac { \cos x ^ { 2 } } { 1 }$ = cos 0 = 1.