Calculus
1 Hour Exam 1 - Math
220 Fall, 2011
1. |
Circle true if the given statement is always true. Otherwise circle false. a. Given a function g, if | g(x) | ≤ x4 for all x then lim g(x) = 0. x→0 b. If the point (-4, ¼) is on the graph of an odd function g then (-1/4, 4) is another point on the graph of g. c. Given a function g, if lim [g(x) – g(4)]/(x – 4) exists then g is continuous at 4. x→4 d. If a function g is continuous at 0 then lim g(x) = 0. x→0 e. A function which is continuous at a point a must also be differentiable at a. f. If a function is one-to-one then g(1) = 1. Answers: a. T b. F c. T d. F e. F f. F |
2. |
Given the graph y = f(x) and six possible choices for graphs of f ’(x) then circle the correct graph of f ‘(x) for the given graph y = f(x). |
3. |
Let f(x) = 4x3 + 2. Use the definition of a derivative as a limit to prove that f ‘(x) = 12 x2. Show each step in your calculation and be sure to use proper terminology in each step of your proof. |
4. |
Suppose that f and g are one-to-one functions which take on the following values. f(-2) = 2, f(-1) = ½, f(0) – ½, f(1) = -2, f(2) = -4 g(-2) = -4, g(-1) =- -2, g(0) – ½, g(1) = ½ , g(2) = 2 What is the value of f-1 ( g-1(-4) ) ? Answer: 1 |
5. |
State the domain of each function. a. f(x) = cos-1 (x) b. g(x) = (8 – x) / ln(x – 4) c. h(x) = √ (x2 + 9) Answers: a. [ -1, 1 ] b. ( 4, 5 ) U ( 5, ∞ ) c. ( -∞ , ∞ ) Click here to continue with this exam. |