tut3 - MATH 237 Tutorial 3 Wednesday May 24th 2006 Partial...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
MATH 237 Tutorial 3 Wednesday, May 24th, 2006 Partial Derivatives, Tangent Plane and Linear Approximation 1) Let f : R 2 R be defned by f ( x, y ) = xy 2 x 2 + y 2 For ( x, y ) 6 = (0 , 0) and f (0 , 0) = 0 . a) Determine ∂f ∂x at ( x, y ) 6 = (0 , 0). b) Determine ∂f ∂x (0 , 0). c) Determine whether ∂f ∂x is continuous at (0 , 0). 2) ±ind the equation oF the tangent plane to the surFace z = 1 1 + xy at (1 , - 2 , - 1). ±ind the point in which this plane intersects the z -axis. 3) ±ind ∂z ∂x and ∂z ∂y iF z is defned implicitly as a Function oF x and y by the equation x 3 + y 3 + z 3 + 6 xyz = 1. 4) Use the linearization For
Background image of page 1
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

Ask a homework question - tutors are online