Calculus

Find the equation of the tangent line plane and normal line to the surface z = ry at the point (2, 1, 4). Normal line( parametric equations x = xo + tn. yiat Y = YO Icto.y.,)1 ..7=z7„-1 Find the directional derivative of the function I at P in the direction of a. x, y. = tan -I (Y-); P(-2,2) a= -i- j. .x- Use Lagrange multipliers to find the maximum and minimum value off subject to the given constraint. Also, find the points at which these extreme values occur. j.,z)= 2x+y-2::: x2 +y2 +z2 =4 Use a double integral to find the area of the region R enclosed 1 between the parabola y=— 2x-, and the line 1: = 2x a2 IX COS xydyciv • 6 Evaluate the triple integral 2xy2 3db Over the rectangular box G define by the inequalities: -1 _c .v 5 2, 0 ‹. y < 3. 0 Lz