Calculus MCQs Question and Answer in Engineering Maths

The parabolic arc y = √x, 1 ≤ x ≤ 2 is revolved around the x-axis. The volume of the solid of revolution is

Which of the following functions would have only odd powers of x in its Taylor series expansion about the point x = 0?

A function f(x) = 1 - x² + x³ is defined in the closed interval [-1, 1]. The value of x in the open interval (-1, 1) for which the mean value theorem is satisfied, is

For 0 ≤ t < $$\infty $$, the maximum value of the function f(t) = e^-t - 2e^-2t occurs at

Let x be a continuous variable defined over the interval $$\left( { - \infty ,\,\infty } \right)$$  , and f(x) = e^-x-e-x . The integral $${\text{g}}\left( {\text{x}} \right) = \int {{\text{f}}\left( {\text{x}} \right){\text{dx}}} $$    is equal to

Divergence of vector field \[\overrightarrow {\rm{V}} \left( {{\rm{x}},\,{\rm{y}},\,{\rm{z}}} \right) = - \left( {{\rm{x}}\cos {\rm{xy}} + {\rm{y}}} \right){\rm{\hat i}} + \left( {{\rm{y}}\cos {\rm{xy}}} \right){\rm{\hat j}} + \left[ {\left( {\sin {{\rm{z}}^2}} \right) + {{\rm{x}}^2} + {{\rm{y}}^2}} \right]{\rm{\hat k}}\]             is

One of the roots of the equation x³ = j, where j is the positive square root of -1, is

The value of the integral $$\int\limits_{ - \infty }^\infty {\frac{{{\text{dx}}}}{{1 + {x^2}}}} $$  is

If $${\text{f}}\left( {\text{x}} \right) = \frac{{2{{\text{x}}^2} - 7{\text{x}} + 3}}{{5{{\text{x}}^2} - 12{\text{x}} - 9}},$$     then $$\mathop {\lim }\limits_{{\text{x}} \to 3} {\text{f}}\left( {\text{x}} \right)$$  will be

For two non-zero vectors $$\overrightarrow {\text{A}} $$ and $$\overrightarrow {\text{B}} $$, if $$\overrightarrow {\text{A}} $$ + $$\overrightarrow {\text{B}} $$ is perpendicular to $$\overrightarrow {\text{A}} $$ - $$\overrightarrow {\text{B}} $$ then,