oldmidterm1 - . [3] Answer 2 FULL-SOLUTION PROBLEMS. In...

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

View Full Document Right Arrow Icon
Student number Name [SURNAME(S), Givenname(s)] MATH 100 (Section 103) Midterm Test 1(X) 2009 Oct 09 This is a closed book examination: no books, notes, electronic memory or communication de- vices are allowed. CALCULATORS AND CELL PHONES ARE NOT ALLOWED. Use backs of pages if necessary, but label clearly. 1. SHORT ANSWER QUESTIONS. If an answer box is provided, put your answer in it, but show your work also. Each question is worth 3 marks, but not all questions are of equal diFculty. At most 1 mark will be given for an incorrect answer. Unless otherwise stated, it is not necessary to simplify your answers. Marks (a) Evaluate (or determine that the limit does not exist) [3] lim x 3 x 2 - 9 x 2 - 6 x + 9 . Answer (b) Evaluate (or determine that the limit does not exist) [3] lim x →∞ 2 x 3 + 5 x x 3 - x 2 + 4 . Answer
Background image of page 1

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

View Full DocumentRight Arrow Icon
(c) Evaluate (or determine that the limit does not exist) lim x 0 x 2 sin 2 5 x . [3] Answer (d) Diferentiate e 3 x 2 . [3] Answer (e) Determine ( g/f ) 0 (3), iF g (3) = 1, g 0 (3) = - 2, f (3) = 4, f 0 (3) = - 3. [3] Answer (F) ±ind the second derivative oF e - x cos x and simplify your answer
Background image of page 2
Background image of page 3

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

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

Unformatted text preview: . [3] Answer 2 FULL-SOLUTION PROBLEMS. In questions 24, justify your answers and show all your work. If you need more space, use the back of the previous page. 2. Carefully prove that 2 x 4-x 3 + 2 x 2-1 has a root between x =-1 and x = 1. [5] 3. Use the defnition of the derivative to prove that if f ( x ) is a diFerentiable function [6] and g ( x ) = x 2 f ( x ), then g ( x ) = x 2 f ( x ) + 2 x f ( x ). No credit will be given for using the Product Rule. 3 4. Find a point on the curve y = 16-x 2 that is below the x-axis, such that the tangent [5] line through that point also passes through the point (5 , 0), or determine that no such point exists. 5. Let [6] f ( x ) = ( ax + b if- < x 2, c + ( x-2) 2 sin 1 ( x-2) 2 if 2 < x < , and determine all values (if any exist) of the constants a , b , and c so that f ( x ) is continuous for all x . (Remember to justify your answer.) 4...
View Full Document

Page1 / 4

oldmidterm1 - . [3] Answer 2 FULL-SOLUTION PROBLEMS. In...

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