Calculus home work help
Name: College ID: Thomas Edison State University Calculus I (MAT-231) Section no.: Semester and year: Written Assignment 2 Answer all assigned exercises, and show all work. Each exercise is worth 5 points. 1. Use numerical and graphical evidence to conjecture values for the following limit. If possible, use factoring to verify your conjecture. 2 x x 2 x 2 2 x lim 2. Use the given graph to identify each limit, or state that it does not exist. (a) lim f ( x ) x 1 WA 2, p. 1 (b) (c) lim f ( x) x 1 lim f ( x ) x 1 lim f ( x) (d) x 2 (e) x 2 (f) lim f ( x ) lim f ( x) x 2 lim f ( x) (g) x 3 (h) x 3 lim f ( x) 3. Evaluate the indicated limit, if it exists. Assume that lim x 1 lim x 0 sin x 1. x x2 x 2 x2 3x 2 sin x 1. 4. Evaluate the indicated limit, if it exists. Assume that x 0 x lim lim x 0 tan x x WA 2, p. 2 sin x 1. 5. Evaluate the indicated limit, if it exists. Assume that x 0 x lim 2x x 0 3 x 9 lim 6. Evaluate the indicated limit, if it exists. Assume that lim f ( x), x 1 where lim x 0 sin x 1. x x 2 1 if x 1 f ( x) 3 x 1 if x 1 sin x 1. 7. Evaluate the indicated limit, if it exists. Assume that x 0 x lim tan x x 0 5x lim 8. Use the given position function f(t) to find the velocity at time t = a. f (t ) t 2 2, a 0 1 cos 2 x sin x 1, lim . x2 9. Given that x 0 x quickly evaluate x 0 lim 10. Determine where f is continuous. If possible, extend f as in example 4.2 (See Section 1.4) to a new function that is continuous on a larger domain. f ( x) 4x x x 2 2 WA 2, p. 3 11. Determine where f is continuous. If possible, extend f as in example 4.2 (See Section 1.4) to a new function that is continuous on a larger domain. f ( x ) x cot x 12. Determine where f is continuous. If possible, extend f as in example 4.2 (See Section 1.4) to a new function that is continuous on a larger domain. sin x f ( x) x 1 if x 0 if x 0 13. Determine the intervals on which f is continuous. f ( x) x 2 4 14. Use the given graph to identify all intervals on which the function is continuous. 15. Determine the limit (answer as appropriate, with a number, , -, or does not exist). lim x sec 2 x x /2 WA 2, p. 4 16. Determine the limit (answer as appropriate, with a number, , -, or does not exist). 2 x 2 x 1 lim 2 x 4 x 3x 1 17. Determine the limit (answer as appropriate, with a number, , -, or does not exist). lim e ( x1)/( x 2 2) x 18. Determine all vertical and slant asymptotes. x2 1 y x 2 100 2 3(0.4)t mm. 19. Suppose that the length of a small animal t days after birth is What is the length of the animal at birth? What is the eventual length of the animal (i.e., the length as t )? h(t ) 20. Symbolically find in terms of . lim(3 4 x) 7 x 1 WA 2, p. 5
