Chapter 3.2, Problem 2QR

3. Use the Squeeze theorem to prove that lim x sin X-0 (Hint: Use f(x) = |x| and g(x) = -[x])) = 0. Explain thoroughly.

1. : steps and setup. Use the limit definition to find the derivative of f(x) = 5x? + 2x – 7 at x = -2. Show all f(a + h) – f(a) lim h→0 h

Solve this question , I AM STUCKED

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.

Use the definition of the limit of a function of two variables to verify the limit.

explain in detail

Which of the following statement/s is/are true about the function whose graph is shown below? A x) A. lim f(x) = lim f(x) = 0. x-2+ x-2 B. lim f(x) does not exist. x--1 C. lim f(x) f(-5). x--5+ D. The function is defined at x = -1. A В C

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.

Explain thoroughly on paper thanks :). The exercise 6-1 is referring to the Q'S a-h in the first pic