Calculus MCQs Question and Answer in Engineering Maths

For a small value of h, the Taylor series expansion for f(x + h) is

The divergence of the vector field \[{\rm{3xz\hat i}} + 2{\rm{xy\hat j}} - {\rm{y}}{{\rm{z}}^2}{\rm{\hat k}}\]    at a point (1, 1, 1) is equal to

The right circular cone of largest volume that can be enclosed by a sphere of 1 m radius has a height of

The area enclosed between the curves y² = 4x and x² = 4y is

It is known that two roots of the nonlinear equation x³ - 6x² + 11x - 6 = are 1 and 3. The third root will be

The derivative of f(x) = cos x can be estimated using the approximation \[{\text{f}}'\left( {\text{x}} \right) = \frac{{{\text{f}}\left( {{\text{x}} + {\text{h}}} \right) - {\text{f}}\left( {{\text{x}} - {\text{h}}} \right)}}{{2{\text{h}}}}.\]
The percentage error is calculated as \[\left( {\frac{{{\text{Exact value}} - {\text{Approx value}}}}{{{\text{Exact value}}}} \times 100} \right)\]
The percentage error in the derivative of f(x) at \[{\text{x}} = \frac{\pi }{6}\]  radian choosing h = 0.1 radian is

If \[\overrightarrow {\rm{A}} = {\rm{xy}}{{{\rm{\hat a}}}_{\rm{x}}} + {{\rm{x}}^2}{{{\rm{\hat a}}}_{\rm{y}}},\,\oint\limits_{\rm{c}} {\overrightarrow {\rm{A}} \cdot {\rm{d}}\overrightarrow l } \]     over the path shown in the figure is

The expression \[\mathop {\lim }\limits_{\alpha \to 0} \frac{{{{\text{x}}^\alpha } - 1}}{\alpha }\]   is equal to

It is known that two roots of the non-linear equation x³ - 6x² + 11x - 6 = 0 and 1 and 3. The third root will be

Consider the function y = x² - 6x + 9. The maximum value of y obtained when x varies over the interval 2 to 5 is