University:
Georgia Southern University
Course:
MATH 1441 | Calculus I
Academic year:

2024
Views:

388

Pages:

5
Author:

Jalen W.

Student: Jalen Wilson Date: 07/12/24 Instructor: Neelam Aggarwal Course: Spring 2022 - Calculus I (MATH1441-02F) 1. Suppose that lim f(x) = 3 and lim g(x) = − 5. Find the following limits. x →2 x →2 a. lim [f(x)g(x)] x →2 b. lim [2f(x)g(x)] x →2 lim [f(x)g(x)] = x →2 (Simplify youranswer.) lim [2f(x)g(x)] = x →2 (Simplify youranswer.) lim [f(x) + 2g(x)] = x →2 (Simplify youranswer.) f(x) lim = f(x) − g(x) x →2 (Type a simplified fraction.) c. lim [f(x) + 2g(x)] x →2 f(x) d. lim f(x) − g(x) x →2 Assignment: Section 2.5 Enhanced Assignment 2. a. Graph f(x) = 2 4−x , x≠ −2 7, b. Find lim f(x) and x→ − 2 − x = − 2. lim f(x). x→ − 2 + c. Does lim f(x) exist? Ifso, what isit? Ifnot, whynot? x→ − 2 a. Choose the correct graph below. A. B. 10 y C. 10 y x -10 10 10 10 x -10 -10 b. Find D. y 10 y x -10 -10 10 -10 x -10 10 -10 lim f(x). Select the correct choice belowand, ifnecessary, fill in the answer box in your choice. x→ − 2 − A. lim f(x) = x→ − 2 (Simplify youranswer.) − B. The limit does not exist. Find lim f(x). Select the correct choice belowand, ifnecessary, fill in the answer box in your choice. x→ − 2 A. + lim f(x) = x→ − 2 (Simplify youranswer.) + B. The limit does not exist. c. Does lim f(x) exist? Select the correct choice belowand, ifnecessary, fill in the answer box in your choice. x→ − 2 A. Yes, lim f(x) exists and equals x→ − 2 . (Simplify youranswer.) B. No, lim f(x) does not exist because f( − 2) is undefined. x→ − 2 C. No, lim f(x) does not exist because lim f(x) ≠ lim f(x). x→ − 2 x→ − 2 − x→ − 2 + D. No, lim f(x) does not exist because f( − 2) is not equal to lim f(x) or lim f(x). x→ − 2 x→ − 2 − x→ − 2 + 3. Say whether the function graph below is continuous on [ − 2,7]. Ifnot, where does it fail to becontinuous? 5 y Select the correct answer belowand, ifnecessary, fill in the answer box to complete your choice. A. The graph is not continuous on the interval . 4 (Type your answer in intervalnotation.) B. The graph is not continuous at x= . 3 2 ( Use a comma to separate answers asneeded.) 1 x -3 -2 -1 1 2 3 4 5 6 7 C. The graph is continuous on [ − 2,7]. 8 -1 4. State whether the function graphed is continuous on [ − 1,3]. Ifnot, where does it fail to be continuous andwhy? 6 y 4 2 x -2 2 Is the function continuous on the interval [ − 1,3]? Ifnot, why? A. The function is not continuous at x = 1 because of a jump discontinuity. B. The function is continuous on the interval [ − 1,3]. C. The function is not continuous at x = 1 because of a removable discontinuity. D. The function is not continuous at x = 1 because of an oscillating discontinuity. 5. Use the function and the accompanying figure to answer the following questions. 2 a. Is f defined at x = 2? f(x) = x − 3, −1≤x<0 3x, 0