MID TERM #1, MATH 100
Wednesday, October 9, 2002 Student No: Name (Print):
There are 5 pages to this test, check to make sure it is complete. Please put your name and student number at the top of ever
HOMEWORK ASSIGNMENT #7
due in class on Friday, November 8 Student No: Name (Print):
Note: All homework assignments are due in class one week after being assigned. They must be on standard 8 1 11 size
HOMEWORK ASSIGNMENT #8
due in class on Friday, November 22 Student No: Name (Print):
Note: All homework assignments are due in class one week after being assigned. They must be on standard 8 1 11 size
SOLUTIONS TO HOMEWORK ASSIGNMENT #2
1. Compute the following limits: sin(-x) 3 1 + 2x - 1 - 2x (b) lim (c) lim (a) lim x0 sin 3x x0 0 (sin )2 x 2 t z +1 cos x (d) lim (e) lim 2 (f) lim 2 t0 t + sin t
SOLUTIONS TO HOMEWORK ASSIGNMENT #3
1. Each of the following questions can be done with little computation. Suppose f (x), g(x) are functions satisfying f (a) = , g(a) = , f (a) = and g (a) = for some
SOLUTIONS TO HOMEWORK ASSIGNMENT #4
1. Find all x such that f (x) = 0, where: (a) f (x) = cos(x2 ). (b) f (x) = sin 2x. (c) f (x) = 3x5 5x3 . (d) f (x) = x3 + 5x2 + 3x. Solutions: (a) f (x) = 2x sin(x
SOLUTIONS TO HOMEWORK ASSIGNMENT #5
1. Each of the following questions can be done with little computation. Enter your answers in the boxes and show any work in the spaces provided. Find derivatives o
SOLUTIONS TO HOMEWORK ASSIGNMENT #6
1. A culture of bacteria is found to contain 104 bacteria per cm3 at the start of an experiment. After 1 day there are 106 bacteria. Assume that the number of bacte
SOLUTIONS TO ASSIGNMENT #7
1. Find the linearizations L(x) of the following functions f (x) near x = 0. (a) f (x) = 25 + x2 + x. (b) f (x) = (1 2x) , where is some constant. (c) f (x) = ln(x + 1 x2 ).
SOLUTIONS TO HOMEWORK ASSIGNMENT #8
1. Graph the following functions showing all work: (a) f (x) = x2 . x1
2
(b) f (x) = ex , < x < . (c) f (x) = xex , < x < . (d) f (x) = x2 e|x| . Solution: (a) Firs
if, ,
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b. The more time students take to nish a midterm examination, the higher their score.
independent variable: 'i ' lTLC I k. Mi 8 r
Dependent variable: 'i rJi t: f 0 ti __
c. "It was hyp
HOMEWORK ASSIGNMENT #6
due in class on Friday, October 25 Student No: Name (Print):
Note: All homework assignments are due in class one week after being assigned. They must be on standard 8 1 11 size
HOMEWORK ASSIGNMENT #5
due in class on Friday, October 18 Student No: Name (Print):
Note: All homework assignments are due in class one week after being assigned. They must be on standard 8 1 11 size
HOMEWORK ASSIGNMENT #4
due in class on Friday, October 4 Student No: Name (Print):
Note: All homework assignments are due in class one week after being assigned. They must be on standard 8 1 11 size p
MID TERM #2, MATH 100
Wednesday, November 13, 2002 Student No: Name (Print):
There are 5 pages to this test, check to make sure it is complete. Please put your name and student number at the top of ev
(1) Use Newtons method to nd critical points of the function y = ex 2x2 . Solution: The critical points are located at x values for which y = f (x) = ex 4x = 0. If there exists any root for f (x) = 0,
SOLUTIONS TO MIDTERM 1: MATH 100, SECTION 107
QUESTION 1: [4 marks] Below you are given the graph of y = f (x) for some function y = f (x). Graph the function y = f (x) assuming that f (0) = -1.
3
2
1
MIDTERM 1: MATH 100, SECTION 109, WEDNESDAY OCT. 7
QUESTION 1: [4 marks] Below you are given the graph of y = f (x) for some function y = f (x). Graph the function y = f (x) assuming that f (0) = 1.
1
SOLUTIONS TO MIDTERM #1: MATH 102, SECTIONS 102 & 105 QUESTION 1: [6 marks] (a) Give the definition of the derivative f (x) of a function f (x). (b) In a few brief sentences give several interpretatio
SOLUTIONS TO MIDTERM #1 QUESTION 1: [10 marks] (a) Give the definition of the derivative f (x) of a function f (x). (b) What is the equation of the tangent line to the graph of y = f (x) at x = a? 1 (
QUESTION 1: Find the derivatives of the following functions. DO NOT TRY TO SIMPLIFY. (a) f (x) = tan(1/x) QUESTION 2: Using only the definition of the derivative find f (x) for the function f (x) = QU
SOLUTIONS TO QUIZ 1 Question 1 [6marks] Let f (x) be the function defined by f (x) = 1 + 1/x, x > 0.
1(a) Find the derivative f (x) using only first principles. 1(b) Find an equation of the tangent li
SOLUTIONS TO QUIZ 2 Question 1 [8 marks] 1(a) Show that lim sin h = 1. h0 h 1 - cos h 1 - cos h 1(b) Show that lim = 0. Hint: multiply top and bottom h0 h h by 1 + cos h and then use a trig identity a
SOLUTIONS TO MID TERM #1, MATH 100
1. [6 marks] Using only the denition of the derivative, and not the rules, nd f (x) for the function f (x) = x2 + 1. Solution: (x + h)2 + 1 x2 + 1 f (x + h) f (x) f
SOLUTIONS TO MID TERM #2, MATH 100
1. [6 marks] (a) Find the derivative of f (x) = arcsin( x). Do not simplify. (b) Find f (x) if f (x) = (ln x)x and simplify. f (x) x1 x+1 and simplify.
(c) Find f (x
HOMEWORK ASSIGNMENT #1
due in class on Friday, September 13 Student No: Name (Print):
Note: All homework assignments are due in class one week after being assigned. They must be on standard 8 1 11 siz