In Exercise, find an equation for the tangent plane and parametric equations for the normal line to the surface at the point $P .$

$$z = 4 x ^ { 3 } y ^ { 2 } + 2 y : P ( 1 , - 2,12 )$$

In Exercise, find an equation for the tangent plane and parametric equations for the normal line to the surface at the point $P .$

$$x ^ { 2 } + y ^ { 2 } + z ^ { 2 } = 25 ; \quad P ( - 3,0,4 )$$

Find equations for the tangent plane and normal line to the given surface at

$$P_0$$

.

$$x ^ { 2 } y ^ { 3 } z ^ { 4 } + x y z = 2 ; P _ { 0 } ( 2,1 , - 1 )$$

(a) How and why did the Soviet Union play a direct role in the affairs of a South Asian country? (b) What was the outcome of that intervention?

Solve $- 2 ( - 4 n + 1 ) + 5 \left( \frac { 2 } { 5 } n - 8 \right) = - 62$

$$n =$$

Find equations for the tangent plane and the normal line to the surface with the equation at the given point.

$$z=\ln \frac{x}{y};\hspace{6pt}P\left(2,2,0\right)$$

In Exercise, find an equation for the tangent plane and parametric equations for the normal line to the surface at the point $P .$

$$z = x ^ { 1 / 2 } + y ^ { 1 / 2 } ; \quad P ( 4,9,5 )$$

Find an equation of tangent plane and parametric equations aof the normal line to the surface at the indicated point.

What are two possible reasons for dating?

What are the three most common causes of female infertility?

Find equations of the tangent plane and normal line to the graph of the given function at the point with specified values of x and y. $f(x, y)=\cos (x / y) \text { at }(\pi, 4)$

In the following exercise, find an equation of the tangent plane and parametric equations of the normal line to the surface at the given point.

$$f(x, y)=x^2 y, \quad(2,1,4)$$

Find equations of the tangent plane and normal line to the surface at the given point. $z=x^{2}+y^{2}-1$ at (2, 1, 4)

Find an equation for the tangent plane and parametric equations for the normal line to the surface at the point P.

$$z = x ^ { 2 } + y ^ { 2 }$$

; P(2, -3, 13)