# Mathematics-I(3110014)

BE | Semester 1  Unit : Functions of several variables

## Q1 (a) Winter-2019   Find the equations of the tenagent plane and normal line to the surface ${x}^{2}+{y}^{2}+{z}^{2}=3$ at the point $\left(1,1,1\right)$.

Unit : Functions of several variables

## Q2 (b) Winter-2019   Discuss the Maxima and Minima of the function $3{\mathrm{x}}^{2}-{\mathrm{y}}^{2}+{\mathrm{x}}^{3}$.

Unit : Functions of several variables

## Q3 (c) Winter-2019   Find the maximum and minimum distance from the point $\left(1,2,2\right)$ to the sphere ${\mathrm{x}}^{2}+{\mathrm{y}}^{2}+{\mathrm{z}}^{2}=36$.

Unit : Functions of several variables

## Q5 (c) Winter-2019   If then show that $\frac{\partial u}{\partial x}+\frac{\partial u}{\partial y}+\frac{\partial u}{\partial z}=0$.

Unit : Functions of several variables

## Q5 (a) Winter-2019   Find the directional derivatives of $\mathrm{f}={\mathrm{xy}}^{2}+{\mathrm{yz}}^{2}$ at the point $\left(2,-1,1\right)$, in the direction of $\mathrm{i}+2\mathrm{j}+2\mathrm{k}$.

Unit : Functions of several variables