m222-pract

m222-pract - Sample of problems (1) Interchanging the...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon

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

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Sample of problems (1) Interchanging the orders of integration for the double integral R π 2 R cos x y sin x dydx gives: (a) R sin x y dy R cos y sin x dx , (b) R cos y sin x dx R 1 y dy , (c) R π 2 y =0 R cos- 1 x y sin x dxdy , (d) R 1 R cos- 1 y y sin x dx dy , (e) R 1 R cos y y sin x dxdy . Answer: (d) (2) Let x ( y,z ) be defined implicitly by xy 3 = 2 y- z . Then ∂x ∂y ¶ 2 + ∂x ∂z ¶ 2 at the point (0 , 1 , 2) has the value (a)- . 2, (b) 0 . 2, (c) 5, (d) 2, (e)- . 5. Answer: (c) (3) Define z = Z ( x,y ) implicitly by x 2 + xy + yz + z 2 = 3 with Z (1 , 2) = 0. The directional derivative at (1 , 2) in the direction of the vector (3 ,- 4) is (a)- . 8, (b)- 8, (c)- 2 . 8, (d) 2 . 8, (e) 0 . 8. Answer: (a) (4) Of the two infinite series A : ∞ X n =1 (- 1) n e- n 2 ln( n + 1) , B : ∞ X n =1 √ n 2 + 4 n 2 (a) both are absolutely convergent (b) both are divergent (c) A is divergent and B is convergent (d) A is absolutely convergent and B is divergent (e) A is absolutely convergent and...
View Full Document

This note was uploaded on 05/01/2008 for the course MATH 222 taught by Professor Karlpeterrussell during the Winter '08 term at McGill.

Page1 / 3

m222-pract - Sample of problems (1) Interchanging the...

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

View Full Document Right Arrow Icon
Ask a homework question - tutors are online