List of top Mathematics Questions on Calculus asked in MET

If $f(x) = \begin{cases} \dfrac{x^{2} - 9}{x - 3}, & x \neq 3 \\ 2x + k, & x = 3 \end{cases}$ is continuous at $x = 3$, then $k$ equals

If $f(x) = \sec x - \cot x$, then $f'\!\left(\dfrac{\pi}{6}\right)$ equals

The area of the region $\{(x,y): x^{2} + y^{2} \le 1 \le x + y\}$ is

The minimum value of $x\log x$ is equal to

If $f''(0) = k$, then $\displaystyle\lim_{x\to 0} \dfrac{2f(x) - 3f(2x) + f(4x)}{x^{2}}$ equals

If $\displaystyle\int_{-1}^{4} f(x)\,dx = 4$ and $\displaystyle\int_{2}^{4} [3 - f(x)]\,dx = 7$, then $\displaystyle\int_{-1}^{2} f(x)\,dx$ equals

$\displaystyle\int \frac{2\,dx}{(e^{x} + e^{-x})^{2}}$ is equal to

If the rate of change in the circumference of a circle is $0.3$ cm/s, then the rate of change in the area of the circle when the radius is $5$ cm is

$\displaystyle\lim_{x\to 0}\frac{(2+x)\sin(2+x) - 2\sin 2}{x}$ is equal to

The function $f(x) = \sin x(1 + \cos x)$, $0 \le x \le \dfrac{\pi}{2}$, has a maximum value when $x$ equals

The area included between the curves $y^{2} = 2x$ and $x^{2} = 2y$ is

If $f(x) = \dfrac{x + \cos x}{x - \cos x}$, then $f'\!\left(\dfrac{\pi}{2}\right)$ equals

$\displaystyle\int_{0}^{1} x\sin(\pi x)\,dx$ is equal to

If $f(x) = \begin{cases} x+1, & x \le 1 \\ 3 - ax^2, & x>1 \end{cases}$ is continuous at $x = 1$, then $a$ is

The area bounded by $y = 1 + \dfrac{8}{x^2}$ and the ordinates $x = 2$ and $x = 4$ is

If $f(x) = \dfrac{\log(1+ax) - \log(1-bx)}{x}$ for $x \neq 0$ and $f(0) = k$, and $f(x)$ is continuous at $x = 0$, then $k$ equals

The value of $a$ for which $f(x) = a\sin x + \dfrac{1}{3}\sin 3x$ has an extremum at $x = \dfrac{\pi}{3}$ is

If $|f(x)|$ is continuous at $x = a$, then $f(x)$

The area in square units enclosed by the curve $x^{2}y = 36$, the $x$-axis and the lines $x = 6$ and $x = 9$ is

$\displaystyle\int_{0}^{\pi/2} \dfrac{\sin^{n}\theta}{\sin^{n}\theta + \cos^{n}\theta}\,d\theta$ is equal to

Derivative of $x^{x}$ is

The minimum value of $x^{2} + \dfrac{1}{1 + x^{2}}$ is at}

If \( f(x) = \begin{cases} x^3 - 3x^2 - 12x + 1, & -1 \le x \le 2 \\ 37 - 2x, & 2 < x \le 3 \end{cases} \), then

$\int_{-\pi/2}^{\pi/2} |\sin x| dx$ is

The function $y = a(1-\cos x)$ is maximum when x is equal to