Calc$3$

Practice questions

Copy and paste all graphs. Include them $if$ possible. Answer the questions with the

process.

Normal and Osculating Planes

Plot the following space curves $on$ Maple. Then find and plot the normal and

osculating planes $on$ the curve for some fixed value $oft(use$ two different plots for

the normal and osculating planes$)$

Normal Plane Equation $att=1$ :

Osculating Plane Equation $att=1$ :

Normal Plane Equation $att=$:

Osculating Plane Equation $att=$:

; for $t>0$

Normal Plane Equation $att=1$ :

Osculating Plane Equation $att=1$ :

Normal Plane Equation $att=2$ :

Osculating Plane Equation $att=2$ : Level Curves

Plot the $3D$ graph $of$ the functions, then plot the level curves $in2D.$ You may use

plot the level curves $in2D$ first then $3Dto$ get $an$ understanding $on$ the behavior $on$

the level curves.

$af(x,y)=\sqrt[\phantom{2}]{9-x^2-y^2}$

$cf(x,y)=-\frac{3y}{x^2+y^2+1}$

$cf(x,y)=sin(xy)$

$df(x,y)=-xy{e}^{-x^2-y^2}$