hwk2 - Math 31BH - Homework 2. Due January 25. Part I. 1. (...

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: Math 31BH - Homework 2. Due January 25. Part I. 1. ( Wednesday, Jan 12. ) Using the- δ definition, show that the sequence x n = n 2 n 2 + 1 , 1 √ n converges and find its limit. 2. ( Friday, Jan 14. ) For the two functions (a) f ( x,y ) = 2- x- 2 y (b) f ( x,y ) = 2- ( x- 1) 2- y 2 answer the following questions: (i) draw the graph in 3-space (ii) sketch the level curves (iii) sketch the cross sections 3. ( Wednesday, Jan 19. ) From the textbook solve the following problems: 1 . 7 . 2 , 1 . 7 . 4( a ) , 1 . 7 . 5 , 1 . 7 . 6 . 4. ( Friday, Jan 21. ) In each of the following, differentiate the function f in the direction of the vector at the given point: (a) f ( x,y ) = x 3 + 2 y 3 , at (1 , 1) in the direction i- j √ 2 . (b) f ( x,y ) = x sin y + y cos x at (0 ,π/ 2) in the direction- 3 5 i + 4 5 j . 5. ( Friday, Jan 21. ) Consider the function f ( x,y ) = y x 2 . (i) Draw the level curves of this function; (ii) using your knowledge of one variable calculus, find the tangent at P...
View Full Document

This note was uploaded on 03/28/2011 for the course MATH 31B taught by Professor Dragosoprea during the Winter '11 term at UCSD.

Page1 / 2

hwk2 - Math 31BH - Homework 2. Due January 25. Part I. 1. (...

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

View Full Document
Ask a homework question - tutors are online