M 408C Study Guide - Midterm Guide: Lagrange Multiplier, Maxima And Minima, Tangent Space
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Find a vector equation and parametric equations for the line segment that. Find the unit tangent vector r(t) = 4 t i + t2j + tk at the point given by. T(t) at the point on the curve parameterized by t =1. Find and sketch the domain of f (x,y) = 1+ x y2. (7pts) What is the range of f? (3pts) Show that x2 + y2 does not exist. x2 y2 lim(x,y) (0,0) Find all the second partial derivatives of f (x,y) = x3y5 + 2x4y. Find the equation to the tangent plane to the surface given by (1,1,1). z = xy at the. Use the chain rule to find z = x2y3, y = ssint. (do not simplify) Name________________________________ eid_____________ Each numbered problem is worth 10 points. Find the local maximum and minimum values and saddle points of f (x,y) = x4 + y4 4xy +1.
