{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

# vcprac02 - 4 5 Sketch the surface and the normal you have...

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

The University of Sydney School of Mathematics and Statistics Practice Session 2 MATH2061: Vector Calculus Summer School 2012 1. (a) Find grad f if f ( x, y ) = x + 2 xy 3 y 2 . (b) Find grad g if g ( x, y, z ) = e x cos( yz 2 ). (c) Find φ if φ = 1 radicalbig x 2 + y 2 + z 2 . 2. (a) Given that F = 2 xy i + ( x 2 + z 2 ) j + (2 yz + 2 z ) k is conservative, find a scalar function φ such that F = φ . (b) Find the work done by F along any path C from the point P (1 , 1 , 1) to the point Q (1 , 2 , 3) . 3. Let S be the surface defined by z = x 2 + y 2 . (a) Find the outward normal to this surface at the point P : (1 , 1 , 2). (b) Find the equation of the tangent plane to S at P . 4. Find a unit vector normal to the cone z = radicalbig x 2 + y 2 at the point (3 , 4 , 5). Sketch the surface, and the normal you have found.
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: , 4 , 5). Sketch the surface, and the normal you have found. 5. Calculate Curl F if F = x 2 z i − y j + z 3 k . 6. Let F be the vector ±eld F = ze x sin y i + ze x cos y j + e x sin y k . (a) Show that F is conservative and ±nd a potential function for F . (b) Evaluate i C F · d r where C is the curve x = t , y = t 2 , z = t 3 from t = 0 to t = 1. (c) Evaluate i C F · d r where C is the unit circle, centre (0 , 0), taken once anti-clockwise. Copyright c c 2012 The University of Sydney...
View Full Document

{[ snackBarMessage ]}