Test2 - Name: (1 point) 175 section 2, Test 2, 3/1 You have...

Info iconThis preview shows pages 1–8. 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

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

View Full DocumentRight Arrow Icon

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

View Full DocumentRight 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: Name: (1 point) 175 section 2, Test 2, 3/1 You have the full class period to complete the test. If anything seems unclear, please ask. 1. A particle moves along the xy-plane on the path given by x = 2 t , y = t 2 (assume distance is in m and time is in s ). (a) Find the velocity, speed and acceleration of the particle (as functions of t ). (4 points) (b) Say now that the function f ( x,y ) = x 2 + y 2 + 100 gives the temper- ature (in F ) at the point ( x,y ) on the plane. Find the directional derivative of f in the direction of h 1 , 1 i at the point (- 1 , 2). (6 points) (c) What physical quantity does your answer to part (c) represent? (2 points) 1 (d) Treating f as a function of t along the path of the particle, find df/dt at time t = 1. (5 points) (e) What physical quantity does your answer to part (e) represent? (2 points) 2. Match the following functions and graphs. (2 points each) f 1 ( x,y ) = cos( x ) f 2 ( x,y ) = sin( x ) f 3 ( x,y ) = x sin( x ) f 4 ( x,y ) = sin( x + y ) f 5 ( x,y ) = sin( x- y ) x 2 + y 2 . (a) 2 (b) (c) (d) 3 (e) 3. Let f ( x,y ) = p 2 + x 2 + y . For which values of k R does f have a level curve at height k ? Find and sketch the level curves (if they exist) for k =- 1, k = 0, k = 1 and k = 2. (8 points) 4 4. The following picture is the graph of a differentiable function f ( x,y ). Find the sign (i.e. one of positive, negative or zero) of each of f x (2 , 2), f y (2 , 2), f xx (2 , 2), f xy (2 , 2). (5 points) 5. Let f ( x,y,z,t ) = cos( x 2 + y 2 ) z + t 2 . Find f x , f y , f xz and f tt . (6 points) 5 6. Show that the limit of the function f ( x,y ) = x 2- y 2 x + y as ( x,y ) (0 , 0) is 0. (7 points) 7. Show that the limit of the function f ( x,y ) = x 2- y 2 x 2 + y 2 as ( x,y ) (0 , 0) does not exist. (6 points) 6 8. Say f is a differentiable function of x and y , and that x = r cos( ), y = r sin( ). Find f in terms of f x , f y and r and . (5 points) 9. Find the linear approximation to the function9....
View Full Document

This note was uploaded on 09/14/2011 for the course MATH 175 taught by Professor Aldroubi during the Spring '08 term at Vanderbilt.

Page1 / 14

Test2 - Name: (1 point) 175 section 2, Test 2, 3/1 You have...

This preview shows document pages 1 - 8. Sign up to view the full document.

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