Chapter 3.2, Problem 1QR

Consider the following graph of the function f. АУ X-0- lim f(x) = x→0+ -3 -2 -1 4 3+ True False 2 - + 2 Find the following one-sided limits. (If an answer does not exist, enter DNE.) lim f(x) = y = f(x) 3 4 5 6 Determine whether the statement is true or false. lim f(x) = 2 X

7. Identify if the statement is Always True, Sometimes True or Never True. If lim f(x) exists, then lim f(x) = f(2). x-2 x-2 a. b. If lim f(x) = 4 and lim f(x) = 8, then lim f(x) = 6. X-2+ 8. Determine the derivative of f(x) = x² - 6x using the limit definition of the derivative.

explain in detail

4. Let function g: R → R be defined by g(x) = |x|. g(0+ h) - g(0) h g(0+ h) – g(0) B. The value of lim h→0 h C. Your results from Parts A and B imply that g' (0) is undefined. Explain. A. The value of lim h→0+ is equal to 1. Through some combination of pictures and/or words, explain why this is so. is equal to -1. Through some combination of pictures and/or words, explain why this is so.

a)Express the limit as a definite integral. lim (3c-5)Ax, xE[0,1] b) and then evaluate it. Show the work on your notebook, take a picture, and then upload it here. Upload Choose a File

At which value(s) of x will the function be discontinuous? Зх — 2 f (x) = 2x2 + 7x – 4 O A) x = 2/3 O B) x = 2/3, -4 C) x = 1/2, -4 O D) x = 4, 2

Exercise 2. Let f : (1, 00) → R and g : (0, 1) →R be such that g(x) = f(1/x). Prove that lim f(x) = L if and only if lim g(r) = L.