exam1_sols - M ath 2 50 Y our N ame E xam 1 Your S ignature...

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

View Full Document Right Arrow Icon
Math 250 Exam 1 Spring 2007 Your Name Your Signature I 1< t Y [ ~ Student ID Give your answers in exact form. Do not give decimal approximations. Graphing calculators are not allowed. In order to receive credit, you must show your work. Do not do computations in your head. Instead, write them out on the exam paper. Place a box around I YOUR FINAL ANSWER I to each question. If you need more room, use the backs of the pages and indicate to the reader that you have done so. Problem Total Points Score 1 11 2 5 3 10 4 10 5 10 6 10 7 10 8 10 9 10 10 7 11 7 Total 100
Background image of page 1

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

View Full DocumentRight Arrow Icon
Math 250, Spring 2007 Exam 1 Page 1 of 4 1. [11 points total] Answer each of the following as true (T) or false (F). Do not justify your answers. [£] The speed of the curve r =< cos t, sin t, 3t > is < - sin t, cos t, 3 >. OJ The curvature of a circle of radius 2007 is 1/2007. OJ The gradient of f(x, y) is normal to the level curves of f. m If (1,1). is a critical point for .the fu?ction !(:J;,'j/) then (1, 1) is also a <;:.it~c~ P?i?t +lK forthefunctlOng(x,Y)=f(x~y2). (~t( I}I' _ (t~(\ll) i.fll~J l), - l ; VI ~)) tV 3 t' , \ \ : ( 1-)( (I I I ) 2. X I (1 l' ,,) 21 ) ~ l VI ..:>, [1] The function u(x, t) = ~2 + t satisfies the equation Ut = U xx (heat equation). [1] If u is a unit vector tangent at (x, y) to a, level curve of f(x, y) then t~ directional derivative satisfies Duf(x,y) = o. 0 V\ - .(<:'tJ t. I l>A{.te- I ), \J- -e- -A.!\ l t 'v7 d ~ e) ,,-.;J \ (. h .:".-01\ S e { \,. (' ... - JI' [ i J (~1H ..... , ~ b 1 (,II (' f"1 ) [£] ::. fx(x, y) = Jy(x, y) for ~l x, y, ~hen i(x: y) is_a constant. I .- V- ( [, f ,~ .;): '\-t f ~ ~ \. 'f' "1> ._ . .,. t 1 m If in spherical coordinates a point is given by (p, (), ¢) (2, 7r /2, 7r /2), then its rect- angular coordinates are (x,y,z) = (0,2,0). [Jj
Background image of page 2
Image of page 3
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 02/25/2010 for the course MATH 201 taught by Professor Kim during the Spring '07 term at SIU Carbondale.

Page1 / 5

exam1_sols - M ath 2 50 Y our N ame E xam 1 Your S ignature...

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

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