Section 2.2 Enhanced Assignment

Instructor: Neelam Aggarwal Course: Spring 2022 - Calculus I (MATH1441-02F) Student: Jalen Wilson Date: 07/11/24 1. For the function​g(x) graphed​here, find the following limits or explain why they do not exist. a. lim g(x) x →1 b. lim g(x) x →3 c. lim g(x) x →5 d. lim g(x) x→3.5 8 a. What is lim g(x)? Choose the correct answer below​and, x →1 if​necessary, fill in the answer box to complete your choice. lim g(x) = A. x→1 lim g(x) does not exist B. x→1 b. What is lim g(x)​? Choose the correct answer below​and, x →3 if​necessary, fill in the answer box to complete your choice. y 6 lim g(x) = A. x→3 4 2 lim g(x) does not exist B. x→3 2 x -2 Assignment: Section 2.2 Enhanced Assignment 2 4 6 8 c. What is lim g(x)? Choose the correct answer below​and, x →5 if​necessary, fill in the answer box to complete your choice. -2 lim g(x) = A. x→5 0 lim g(x) does not exist B. x→5 d. What is lim g(x)​? Choose the correct answer below​and, x→3.5 if​necessary, fill in the answer box to complete your choice. lim g(x) = 1.5 A. x→3.5 ​(Type an integer or a​decimal.) lim g(x) does not exist B. x→3.5 2. Which of the statements a through k about the function y = ​f(x) graphed here are​true, and which are​false? 4 y b. The statement lim f(x) = 3 is false. x →0 c. The statement lim f(x) = 0 is true. x →0 2 x -4 a. The statement lim f(x) exists is true. x →0 -2 2 d. The statement lim f(x) = 2 is false. x →2 4 -2 e. The statement lim f(x) = − 1 is false. x →2 -4 f. The statement lim f(x) exists at every point c in ( − 1,2) is true. x →c g. The statement lim f(x) does not exist is true. x →2 h. The statement f(0) = 3 is true. i. The statement f(0) = 0 is false. j. The statement f(2) = − 1 is false. k. The statement f(2) = 2 is true. 3. Find the following limit. 2 lim − x + 2x − 7 x →6 2 lim − x + 2x − 7 = x →6 4. − 31 ​(Simplify your​answer.) x+2 Find lim . x+7 x →5 x+2 7 lim = x + 7 12 x →5 ​(Simplify your​answer.) 5. Find the limit by substitution. lim 5x(10x − 4) x→ − 1 lim 5x(10x − 4) = 70 x→ − 1 6. Find lim h →0 17h + 1 − 1 h ​(Simplify your​answer.) . 17h + 1 − 1 17 lim = h 2 h →0 ​(Type an integer or a simplified​fraction.) 7. x−4 Find lim . 2 x→4 x − 16 x−4 1 lim = 2 8 x→4 x − 16 ​(Type an integer or a simplified​fraction.) 8. Find the limit. 2 lim x →6 x − 2x − 24 x−6 2 lim x →6 x − 2x − 24 x−6 9. = 10 ​(Type an integer or a simplified​fraction.) 2 Find lim t →9 t + 3t − 108 2 . t − 81 2 t + 3t − 108 7 lim = 2 6 t →9 t − 81 ​(Type an integer or a simplified​fraction.) 10. − 7x − 35 Find lim . 3 2 x→ − 5 x + 5x − 7x − 35 7 lim = − 3 2 25 x→ − 5 x + 5x ​(Simplify your​answer.) 11. Find the following limit. 3 u − 64 lim 4 u→4 u − 256 3 u − 64 lim = 4 u→4 u − 256 12. Find 3 16 ​(Simplify your​answer.) x − 14 . lim x − 196 x→196 x − 14 1 lim = x − 196 28 x→196 ​(Type an integer or a simplified​fraction.) 13. Find the exact value of the following expression for the given value of θ. Do not use a calculator. tan (θ/ 2) if θ = π/ 2 If θ = π/ 2​, then tan (θ/ 2) = 1 . ​(Simplify your answer. Type an exact​answer, using radicals as​needed.) 14. Find the limit. lim (2 sin x − 1) x →0 lim (2 sin x − 1) = −1 x →0 ​(Type an integer or a simplified​fraction.) 15. Find the limit. lim sec x x →0 lim sec x = 1 x →0 ​(Type an integer or a simplified​fraction.) 16. Find the limit. lim x →0 lim x →0 1 + 3x + sin x 3 cos x 1 + 3x + sin x 3 cos x 1 = ​(Type an integer or a simplified​fraction.) 3 17. Suppose that lim ​p(x) = 7​, lim ​r(x) = 0​, and lim ​s(x) = − 2. Find the limits in parts​(a) through​(c) below. x→ − 2 x→ − 2 x→ − 2 a. lim (p(x) + r(x) + s(x)) = x→ − 2 ​(Simplify your​answer.) 5 b. lim (p(x) • r(x) • s(x)) = x→ − 2 ​(Simplify your​answer.) 0 − 9p(x) + 4r(x) c. lim = s(x) x→ − 2 ​(Simplify your​answer.) 18. Limits of the form lim h →0 63 2 f(x + h) − f(x) h occur frequently in calculus. Evaluate this limit for the given value of x and function f. 2 f(x) = x ​, x = 4 The value of the limit is 19. Find lim h →0 f(x + h) − f(x) h 8 . ​(Simplify your​answer.) for the given function and value of x. ​f(x) = − 3x − 4​, x = 4 f(x + h) − f(x) The lim for ​f(x) = − 3x − 4​, x = 4 is h h →0 ​(Type an integer or a simplified​fraction.) 20. −3 . f(x) − 3 If lim = 2​, find lim f(x). x−6 x →7 x →7 lim f(x) = x →7 5 ​(Type an integer or a simplified​fraction.)