{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Math_100_and_180_December_2008

# Math_100_and_180_December_2008 - December 2008 Marks[42 1...

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

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

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

View Full Document
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
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

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.

{[ snackBarMessage ]}

### Page1 / 13

Math_100_and_180_December_2008 - December 2008 Marks[42 1...

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

View Full Document
Ask a homework question - tutors are online