Math_100_and_180_December_2008 - December 2008 Marks [42]...

Info iconThis preview shows pages 1–4. Sign up to view the full content.

View Full Document Right Arrow Icon
December 2008 Mathematics 100/180 Page 2 of 13 pages Marks [42] 1. Short-Answer Questions. Put your answer in the box provided but show your work also. Each question is worth 3 marks, but not all questions are of equal diFculty. ±ull marks will be given for correct answers placed in the box, but at most 1 mark will be given for incorrect answers. Unless otherwise stated, it is not necessary to simplify your answers in this question. (a) Evaluate lim x 1 x 2 - x x 2 - 1 or determine that this limit does not exist. Answer (b) Evaluate lim x →∞ x 3 + 5 x 2 x 3 - x 2 + 4 or determine that this limit does not exist. Answer (c) ±ind the derivative of x 3 + e x . Answer Continued on page 3
Background image of page 1

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

View Full DocumentRight Arrow Icon
December 2008 Mathematics 100/180 Page 3 of 13 pages (d) Find the derivative of t 3 cos t . Answer (e) Find the derivative of e x . Answer (f) Find f 0 ( x ), if f ( x ) = arctan( x 3 ). [ Note: Another notation for arctan is tan - 1 .] Answer (g) If x 2 + xy - y 2 = 4, ±nd dy/dx in terms of x and y . Answer Continued on page 4
Background image of page 2
Mathematics 100/180 Page 4 of 13 pages (h) If f ( x ) = (cos x ) x , Fnd f 0 ( x ). Answer (i) Use a linear approximation to approximate 100 . 2. Answer (j) Estimate the size of the error made in the linear approximation above. In other words, Fnd an upper bound for the absolute value of the di±erence between 100 . 2 and the answer to item (i) above. Answer (k) If f ( x ) = x cos( x 2 ), compute f (9) (0). Hint: Use Maclaurin series. Answer
Background image of page 3

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

View Full DocumentRight Arrow Icon
Image of page 4
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 10/02/2010 for the course MATH 100 math 100 taught by Professor Lior during the Fall '10 term at The University of British Columbia.

Page1 / 13

Math_100_and_180_December_2008 - December 2008 Marks [42]...

This preview shows document pages 1 - 4. Sign up to view the full document.

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