List of top Engineering Mathematics Questions on Calculus asked in AP PGECET

Evaluate the limit $$ \lim_{x \to \infty} \frac{\sin x}{x} $$

If \(f = \text{Tan}^{-1}(xy)\) then \((\frac{\partial f}{\partial x})_{(1,2)}\) = _____ .

Let S be a closed surface for which \( \oiint_S \vec{r} \cdot \hat{n} \, dS = 1 \), then the volume enclosed by the surface is ____ .

From the given data value of $\int_{1}^{2} \frac{1}{x} dx$ using Simpson’s 1/3rd rule is

The function $f(x,y) = x^2 + y^2 - xy - x - y + 5$ has
Evaluate the limit: $$ \lim_{x \to 0} \left( x - \sin x \right) \left( \frac{1}{x} \right) $$
In the Taylor series expansion of $e^x$ about $x = 2$, the coefficient of $(x - 2)^4$ is

The Laurent series of $ f(z) = \frac{z}{(z^2+1)(z^2+4)} $ for $ |z|<1 $ is:

The function $ (1 + \cos x) \sin x $ is maximum at
$\lim_{x \to \infty} x \tan \left( \frac{1}{x} \right) = $ _____
$\int_{-\pi/6}^{\pi/6} \frac{(\sin x)^5 (\cos x)^3}{x^4} dx =$
Evaluate $\oint_C (y^2 dx - x^3 dy)$, where $C$ is the positively oriented circle of radius 2 centered at origin.
$f(x) = 2x^2 - 2x + 6$ will have a minimum value at $x=$ _____
If $f(x)$ is differentiable function in x then it is
As per Green's theorem $\oint_C Mdx + Ndy = \iint_R (_____)dxdy$