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 every page. Rough work should be done on the backs of the p
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 paper and they must be stapled. Assign2 ments which are
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 paper and they must be stapled. Assign2 ments which ar
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 z 2z - 1 x- x + 1 Solutions: Theses questions use the l
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 a, , , , . (a) Compute the derivative of f (x) + g(x)
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(x2 ) = 0 x = 0 or x2 = n, for some integer n x = n where
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 of the following functions and simplify as much as possi
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 bacteria increases at a rate that is proportional to the num
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 ). Solution: In all cases the linearization near x = 0 is
SOLUTIONS TO HOMEWORK ASSIGNMENT #8
1. Graph the following functions showing all work: (a) f (x) = x2 . x1
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(b) f (x) = ex , < x < . (c) f (x) = xex , < x < . (d) f (x) = x2 e|x| . Solution: (a) First notice that the function is not dened at x = 1. In fa
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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
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c. "It was hypothesized that...infants who spent greater amounts of t
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 paper and they must be stapled. Assign2 ments which are
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 paper and they must be stapled. Assign2 ments which are
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 paper and they must be stapled. Assign2 ments which are
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 every page. Rough work should be done on the backs of the
(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, there should normally be two. Lets start from x0 = 0 t
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.
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Figure 1. The graph of y = f (x) Solutio
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.
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Figure 1. The graph of y = f (x) Solution to
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 interpretations of the derivative of a function f (x). (c) State the
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 (c) Using only the definition of the derivative find f (
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) = QUESTION 3: Shown below is the graph of a function y = f
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 line to the graph of y = f (x) at x = 1/3. Solution to Qu
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 and properties of limits. Solution to Question 1: 1(a) W
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 (x) = lim = lim h0 h0 h h 2+1 2+1 (x + h) x (x + h)2 +
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) for f (x) = arctan Solution: (a) f (x) = (b) 1 1 . 1x
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 size paper and they must be stapled. Assign2 ments which a