Calculus MCQs Question and Answer in Engineering Maths

For the function e^-x, the linear approximation around x = 2 is

The infinite series \[{\text{f}}\left( {\text{x}} \right) = {\text{x}} - \frac{{{{\text{x}}^3}}}{{3!}} + \frac{{{{\text{x}}^5}}}{{5!}} - \frac{{{{\text{x}}^7}}}{{7!}}\,...\,\infty \]       converges to

If the vector function
\[\overrightarrow {\rm{F}} = {{\rm{\hat a}}_{\rm{x}}}\left( {3{\rm{y}} - {{\rm{k}}_1}{\rm{z}}} \right) + {{\rm{\hat a}}_{\rm{y}}}\left( {{{\rm{k}}_2}{\rm{x}} - 2{\rm{z}}} \right) - {{\rm{\hat a}}_{\rm{z}}}\left( {{{\rm{k}}_3}{\rm{y}} + {\rm{z}}} \right)\]
is irrotational, then the values of the constants k₁, k₂ and k₃ respectively, are

Consider a differentiable function f(x) on the set of real numbers such that f(-1) = 0 and |f'(x)| ≤ 2. Given these conditions, which one of the following inequalities is necessarily true for all x\[ \in \] [-2, 2]?

The curve y = x⁴ is

Which one of the following functions is strictly bounded?

A parametric curve defined by \[{\rm{x}} = \cos \left( {\frac{{\pi {\rm{u}}}}{2}} \right),\,{\rm{y}} = \sin \left( {\frac{{\pi {\rm{u}}}}{2}} \right)\]     in the range 0 ≤ u ≤ 1 is rotated about the x-axis by 360°. Area of the surface generated is

Let \[{\rm{g}}\left( {\rm{x}} \right) = \left\{ {\begin{array}{*{20}{c}} { - {\rm{x,}}}&{{\rm{x}} \le 1}\\ {{\rm{x}} + 1,}&{{\rm{x}} \ge 1} \end{array}} \right.\]     and \[{\rm{f}}\left( {\rm{x}} \right) = \left\{ {\begin{array}{*{20}{c}} {1 - {\rm{x,}}}&{{\rm{x}} \le 0}\\ {{{\rm{x}}^2},}&{{\rm{x}} > 0} \end{array}} \right..\]
Consider the composition of f and g i.e. (fog) (x) = f(g(x)). The number of discontinuities in (fog) (x) present in the interval (\[ - \infty ,\]  0) is:

What is \[\mathop {\lim }\limits_{\theta \to 0} \frac{{\sin \theta }}{\theta }\]  equal to?

A cubic polynomial with real coefficients