List of top Mathematics Questions on Calculus asked in AP ECET Agricultural Engg

If \(u=e^{xy}\), then the value of \[ \frac{\partial^2u}{\partial x^2}+\frac{\partial^2u}{\partial y^2} \] at \((1,1)\) is

If \(z=x^2-y^2\), then \[ \frac{1}{x}\frac{\partial z}{\partial x}+ \frac{1}{y}\frac{\partial z}{\partial y} = \]

For what value of \(x\), the function \[ 2x^3+3x^2-36x+10 \] has minimum?

The equation of the tangent to the curve \(y=x^3\) at \((1,1)\) is

Slope of the normal to the curve \[ x^{2/3}+y^{2/3}=2 \] at the point \((1,1)\) is

If \[ y=\sqrt{\sin x+\sqrt{\sin x+\sqrt{\sin x+\cdots}}}, \] then \(\frac{dy}{dx}=\)

\[ \frac{d}{dx}\left(\tan^{-1}\frac{x}{a}\right)= \]

The derivative of \(x^x\) with respect to \(x\) is

The value of \[ \lim_{x\to 1}\left(\frac{x^3-1}{x-1}\right) \] is

The value of \[ \lim_{x\to\infty}\frac{4x^3-x+1}{x^2-4x(1-x^2)} \] is