AIEEE 2003 | Definite Integration Question 268 | Mathematics

$$\mathop {\lim }\limits_{n \to \infty } {{1 + {2^4} + {3^4} + .... + {n^4}} \over {{n^5}}}$$ - $$\mathop {\lim }\limits_{n \to \infty } {{1 + {2^3} + {3^3} + .... + {n^3}} \over {{n^5}}}$$

$${1 \over 5}$$

$${1 \over 30}$$

zero

$${1 \over 4}$$

AIEEE 2003

MCQ (Single Correct Answer)

-1

The value of $$\mathop {\lim }\limits_{x \to 0} {{\int\limits_0^{{x^2}} {{{\sec }^2}tdt} } \over xsinx}$$ is

AIEEE 2003

MCQ (Single Correct Answer)

-1

If $$f\left( y \right) = {e^y},$$ $$g\left( y \right) = y;y > 0$$ and

$$F\left( t \right) = \int\limits_0^t {f\left( {t - y} \right)g\left( y \right)dy,} $$ then :

$$F\left( t \right) = t{e^{ - t}}$$

$$F\left( t \right) = 1t - t{e^{ - 1}}\left( {1 + t} \right)$$

$$F\left( t \right) = {e^t} - \left( {1 + t} \right)$$

$$F\left( t \right) = t{e^t}$$.

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