List of top Statistical Science Questions on Calculus

If $\Delta$ and $\nabla$ be the first forward difference and first backward difference operator respectively, then the expression $(1+\Delta)(1-\nabla)$ is equivalent to :

The process of evaluating a definite integral from a set of tabulated values of the integrand is called:

The formula to solve simple non-linear equation f(x) = 0 by Newton’s Raphson Method is given by :

If $z = f(x, y)$ and $x = e^u + e^{-v$ and $y = e^{-u} - e^v$, then :}

The area under the curve y = cos x on $\left[-\frac{\pi}{2}, \frac{\pi}{2}\right]$ is given by :

A toy manufacturer produces an inexpensive doll (flopsy) and an expensive doll (mopsy) in units of x hundreds and y hundreds respectively. Suppose it is possible to produce the doll in such a way that y = \(\frac{82-10x}{10-x}\) , 0 \(\le\) x \(\le\) 8 and that the company receives twice as much for selling a mopsy doll as for selling a flopsy doll. The level of production for both flopsy and mopsy dolls for which the total revenue derived from selling these dolls is maximized is given by :

If \(x = a(\cos t + t\sin t)\) and \(y = a(\sin t - t\cos t)\), then the value of \(\frac{d^2y}{dx^2}\) is given by :

If \(\lim_{x \to -a} \frac{x^9 + a^9}{x + a} = 9\), then the possible values of a are given by :

The vertical asymptote for \(f(x) = \frac{3x+5{7-x}\) is given by :}

If \(u\) and \(v\) are functions of two independent variables \(x\) and \(y\), then the determinant \[ \begin{vmatrix} \dfrac{\partial u}{\partial x} & \dfrac{\partial u}{\partial y} \\ \dfrac{\partial v}{\partial x} & \dfrac{\partial v}{\partial y} \end{vmatrix} \] is called:

Let $f$ be differentiable on $(a, b)$ and continuous on $[a, b]$. Then there is at least one $c$ in $(a, b)$ such that $f'(c) = \frac{f(b) - f(a)}{b-a}$. This is the statement of}

Let $f$ be a function which is twice differentiable at $x = c$ and $f'(c) = 0$. If $f''(c) > 0$, then

Which of the following is a method to solve simple non-linear equations by numerical method

Which of the following is a method for numerical integration?

If the interval of differencing being unity and $\Delta$ be the forward difference operator, then for constants $a$ and $b$, the value of $\Delta (ab^x)$ is given by

The general solution of $\frac{d^2 y}{dx^2} - \frac{dy}{dx} - 6y = 0$ is given by}

A particular integral of the differential equation $\frac{d^2 y}{dx^2} + 3 \frac{dy}{dx} + 4y = 3x + 2$ is given by}

The solution of the differential equation $\frac{dy}{dt} = ky$, $k > 0$ is given by}

The necessary and sufficient condition for the differential equation, $M(x, y) dx + N(x, y) dy = 0$ to be exact is given by

The solution of the initial value problem $\frac{dy}{dx} = -6xy \ ; \quad y(0) = 7$ is given by}

If $z = 3x^2 y^3$, $x = t^4$ and $y = t^2$, then using chain rule $\frac{dz}{dt}$ is given by}

The value of $\int \frac{\cos x}{\sin^2 x} \, dx$ is given by}

The value of $\int_0^2 x(x^2 + 1)^3 \, dx$ is given by

The value of $\iint_R y^2 x \, dy \, dx$ over the rectangle, $R = \{(x, y) : -3 \le x \le 2, 0 \le y \le 1\}$ is given by}

The curvature of a circle of radius 'a' is