The function, $y=6s\frac{i{n}^{2x}}{3}$ has $an$ amplitude $o.$

and a period $of$

State whether the following function $is$ odd, even $or$ neither:

Using the Table below for Questions $11-20$:

Evaluate ${\displaystyle \underset{0}{\overset{}{}}}\frac{2}{3^2}{x}^5{e}^{-x}dx$

Evaluate ${\displaystyle \underset{0}{\overset{\frac{}{2}}{}}}{2}^3\sqrt[\phantom{2}]{4-si{n}^2}d$

Evaluate ${\displaystyle \underset{0}{\overset{}{}}}6x^{\frac{1}{2}}{e}^{-x^2}dx$

Evaluate ${\displaystyle \underset{0}{\overset{}{}}}3x^2{e}^{-2x}dx$

Evaluate ${\displaystyle \underset{0}{\overset{}{}}}{2}^2{x}^{\frac{1}{2}}{e}^{-x^2}dx$

Evaluate $I=2{\displaystyle \underset{0}{\overset{1}{}}}{x}^5(1-x{)}^{4}dx$

Evaluate $I=3{\displaystyle \underset{0}{\overset{\frac{}{2}}{}}}si{n}^{3}co{s}^{3}dx$

Evaluate $I={\displaystyle \underset{0}{\overset{1}{}}}3x^4(1-x{)}^{4}dx$

Evaluate $I={\displaystyle \underset{0}{\overset{1}{}}}\frac{1}{3}{x}^2\sqrt[\phantom{2}]{1-x^2}dx$

Evaluate $I={\displaystyle \underset{0}{\overset{1}{}}}\frac{}{2}{x}^4\sqrt[\phantom{2}]{1-x^2}dx$ Determine the direction from the point $(1,1,0)$ which gives the greatest rate $of$ increase $of$ the function

$=(x+3y{)}^2+(2y-z{)}^2.$

Calculate the unit normal vector $to$ the surface $x^3{y}^2+4x{z}^2+2x{y}^{2}z+4=0,at$ point $(1,2,-1)$

Determine gradient $at$ the point $P(1,4,2),If=x^{2}y{z}^3+x{y}^2{z}^2.$

Derive $an$ expression for grad $(A.B),$ given that $A=x^{2}zi+xyj+y^{2}zk$ and $B=y{z}^{2}i+xzj+x^{2}zk$

Determine grad $(A.B)at$ point $(1,3,2)$ from question $(39)$ above.

Evaluate ${\displaystyle \underset{v}{\overset{\phantom{}}{}}}Fdv$ where $Vis$ the region bounded $by$ the planes $x=0,x=2$;$y=0,y=4$;$z=0,z=5$ and

$F=2$xyi$+z^{2}j-3x^{2}k$

A scalar field, $V=xyz$ exist over the curved surface $S$ given $by{x}^2+2y^2=3$ between the plane $z=$

$0$ and $z=4in$ the first octant. Evaluate ${\displaystyle \underset{s}{\overset{\phantom{}}{}}}Vds.$

Find the directional derivative $of$ the function $=x^{2}z+2x{y}^2+y{z}^{3}at$ the point $P(2,1,-1)in$ the

direction $of$ the vector $A=i+3j-2k.$

Determine Curl $Fat$ the point $(2,1,3)$ given that, $F=z{e}^{2xy}i+2$xzCosyj$+(x+y)k$

$If=xyz-y^{2}z+x^2{z}^2,$ determine divgrad$at$ point $(2,3,1).$

Determine the unit normal $to$ the surface $xyz+x^{2}z-3yz-5=0$

$IfA=x^{2}yz+x{z}^2$ and $B=x{y}^{2}z-z^2,$ evaluate grad$(AB)at$ the point $(2,-1,3).$

$IfA=2x^{2}yi-2(x{y}^2+y^{3}z)j+4y^{2}zk,$ determine grad,$A$

$IfV=x{y}^2+y{z}^2,$ evaluate