# mat237t1a - 1(a[6 marks Suppose l is the tangent line to...

This preview shows pages 1–3. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: 1. (a) [6 marks] Suppose l is the tangent line to the curve at (1, 1, 1), ) , , ( ) ( : 3 2 t t t t C = g and π is the plane tangent to the surface at . Find the 1 2 3 2 2 − = + + z z y x y x ) 1 , , 1 ( − − equation of the line through (1, 1, 1) that is parallel to the plane π and orthogonal to the line l . (b) [4 marks] Find a real valued function whose 0-level set is the image ) , , ( z y x F S of the map defined by 3 2 : R R → f ) 2 1 , , ( ) , ( u v u v u v u − + − = f . 2 2. (a) [5 marks] Define the function by R R f → 2 : ⎩ ⎨ ⎧ + = ) ln( ) , ( 2 2 y x y y x f ) , ( ) , ( ) , ( ) , ( = ≠ y x for y x for . Let u = be a unit vector. Write, using the definition (as a limit!), the directional ) , ( b a derivative of f in the direction of u at the point (0, 0). In what direction(s), if any, does exists? Is f of class on f u ∂ 1 C 2 R ? Justify your answers with virtually no calculations....
View Full Document

{[ snackBarMessage ]}

### Page1 / 8

mat237t1a - 1(a[6 marks Suppose l is the tangent line to...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online