Calculus MCQs Question and Answer in Engineering Maths

What is curl of the vector field 2x²yi + 5z²j - 4uyzk?

A rail engine accelerates from its stationary position for 8 seconds and travels a distance of 280 m. According to the Mean Value Theorem, the speedometer at a certain time during acceleration must read exactly

Let f(x) = x e^-x. The maximum value of the function in the interval (0, \[\infty \]) is

The contour on the x - y plane, where the partial derivative of x² + y² with respect to y is equal to the partial derivative of 6y + 4x with respect to x, is

Consider the following equations
\[\begin{gathered} \frac{{\partial {\text{V}}\left( {{\text{x, y}}} \right)}}{{\partial {\text{x}}}} = {\text{p}}{{\text{x}}^2} + {{\text{y}}^2} + 2{\text{xy}} \hfill \\ \frac{{\partial {\text{V}}\left( {{\text{x, y}}} \right)}}{{\partial {\text{y}}}} = {{\text{x}}^2} + {\text{q}}{{\text{y}}^2} + 2{\text{xy}} \hfill \\ \end{gathered} \]
where p and q are constants. V(x, y) that satisfies the above equations is

$$\mathop {\lim }\limits_{{\text{x}} \to 0} \frac{{{{\text{e}}^{\text{x}}} - \left( {1 + {\text{x}} + \frac{{{{\text{x}}^2}}}{2}} \right)}}{{{{\text{x}}^3}}} = ?$$

The quadratic approximation of f(x) = x³ - 3x² - 5 a the point x = 0 is

The following inequality is true for all x close to 0.
\[2 - \frac{{{{\text{x}}^2}}}{3} < \frac{{{\text{x}}\sin {\text{x}}}}{{1 - \cos {\text{x}}}} < 2\]
What is the value of \[\mathop {\lim }\limits_{{\text{x}} \to 0} \frac{{{\text{x}}\sin {\text{x}}}}{{1 - \cos {\text{x}}}}?\]

The series \[\sum\limits_{{\text{n}} = 0}^\infty {\frac{1}{{{\text{n}}!}}} \]  converges to

The quadratic approximation of f(x) = x³ - 3x² - 5 a the point x = 0 is