math-51-f09-hw7-revised

# math-51-f09-hw7-revised - 1 Problem set 7 1 Compute the...

This preview shows pages 1–2. 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 Problem set 7 1. Compute the first-order partial derivatives of f ( x, y ) = xy 2 by explicitly evaluating the limits coming from the definition. 2. Let f ( x, y, z, w ) = (1 , z + w, 1 x 2 + y 2 ) and let a = (3 , 4 , , 0) . Compute D f ( a ) . 3. Let g ( s, t ) = (3 cot s t , 2 s ) and let a = (1 , 1) . Compute D g ( a ) . 4. Let F ( x, y, z ) = xz sin(2 y ) + ye z . (a) Find all the mixed partial derivatives of F and verify that Clairaut’s Theorem holds. (b) Is F zxy = F xzy ? Could you have known this without explicitly performing the calculation? (c) is F yzy = F yyz ? 5. For what real number a, b , and c does the function f ( x, y ) = ax 2 + bxy + cy 2 satisfy the partial differential equation f xx + f yy = 0? 6. Let S and P be the hemisphere and plane defined, respectively, by S = { ( x, y, z ) ∈ R 3 vextendsingle vextendsingle x 2 + y 2 + z 2 = 6 and z ≥ } P = { ( x, y, z ) ∈ R 3 vextendsingle vextendsingle x = 2 } ....
View Full Document

{[ snackBarMessage ]}

### Page1 / 2

math-51-f09-hw7-revised - 1 Problem set 7 1 Compute the...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online