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- Find all points on the surface z = 2 + xy at which the normal line is parallel to the linex = 3 + 2t, y = −1 − 3t, z = 2 + 4tFind the normal line to f(x)=ax^2-3ax at x=2. Assume that a is a positive constant.Find the average value of f(x,y)=yx^2 over the rectangle RR with vertices (−2,0),(−2,5),(2,5),(2,0).
- If F = xi + -4yj +x2k determine the flux of F through S, where S is the portionof z2 = x2 + y2, restricted for 1 greater than or equal to z greater than or equal to 3. Assume the normals point outward.Suppose X has the B(20, 0.5) distrubution. Using normal approximation for X with the continuity correction calculate the P(x < 6)Suppose X has the B(20, 0.5) distrubution. Using normal approximation for X with the continuity correction calculate the P(x ≤ 10)
- Find an equation of the tangent plane and symmetric equations of the normal line to thesurface zx2 − xy2 − yz2 = 18 at the point (0, −2, 3)Find the normal vector to the level curve f(x, y) = c at P.f(x, y) = -2x - 3yc = 4, P(0, 0)find equations for the(a) tangent plane and(b) normal line at the point P0 on the given surface. x2 + y2 + z2 = 3, P0(1, 1, 1)