List of top Statistical Science Questions on Calculus asked in ICAR AIEEA (PG)

Find the vertical asymptotes of \[ f(x)=\frac{-8}{x^2-4}. \]

A liquid form of penicillin manufactured by a pharmaceutical company is sold in bulk at a price of $\$200$ per unit. If the total production cost (in dollars) for $x$ units is \[ C(x)=500{,}000+80x+0.003x^2, \] and the production capacity of the firm is at most $30{,}000$ units in a specified time, then how many units of penicillin must be manufactured and sold during that specified time to maximize the profit?

Find the vertical asymptotes of \[ f(x)=\frac{-8}{x^2-4}. \]

The line $y = L$ is a horizontal asymptote of the graph of the function $f$ if

Find the interval in which the graph of the function given by $f(x) = x^4 - 4x^3 + 10$ is concave up.

If the interval of differencing being unity and $\Delta$ be the forward difference operator, then the value of $\Delta\left(\frac{x^2}{x^2}\right)$ is given by

Evaluate the integral $I = \int_0^1 \frac{1}{1+x} dx$ by using Simpson's one-third rule with $h = 0.5$

Find the value of $\int_{-1}^2 |x| dx$

Find the interval in which the graph of the function given by $f(x) = x^4 - 4x^3 + 10$ is concave up.

The line $y = L$ is a horizontal asymptote of the graph of the function $f$ if

The point at which the tangent to the curve $y = x^3 - 3x^2 - 9x + 7$ is parallel to the x-axis is

The value of $\int_0^\infty x^7 e^{-x^2} dx$ is

The formula to solve simple nonlinear equation $f(x) = 0$ by Newton's Raphson Method is given by

Evaluate the integral $I = \int_0^1 \frac{1}{1+x} dx$ by using Simpson's one-third rule with $h = 0.5$

Find the value of $\int_{-1}^2 |x| dx$

The formula to solve simple nonlinear equation $f(x) = 0$ by Newton's Raphson Method is given by

If the interval of differencing being unity and $\Delta$ be the forward difference operator, then the value of $\Delta\left(\frac{x^2}{x^2}\right)$ is given by

Evaluate $\lim_{x \to +\infty} \frac{x}{\sqrt{x^2 + 1000}}$

If $z = 3x^2y - x \sin xy$, then:

If $z = 3x^2 y - x\sin(xy)$, then

The value of the integral $I = \int_{0}^{1} \frac{1}{1+x} dx$ by using Simpson's one-third rule with $h = 0.5$ is

Find constants a and b so that $\lim_{x \to 0} \left( \frac{a}{2x} + \frac{a}{2} + b \right) = 1$

Find the interval in which the graph of the function given by $f(x) = x^4 - 4x^3 + 10$ is concave up.

The line $y = L$ is a horizontal asymptote of the graph of the function $f$ if

The point at which the tangent to the curve $y = x^3 - 3x^2 - 9x + 7$ is parallel to the x-axis is