Question

1. (a) Make a table, rounding all entries to four decimal digits, to estimate the instantaneous rate of change of f(x) = x° at x = 1. Round your final answer to three decimal digits (b) Briefly describe how the entries in your table relate to the graph f(x)= x. In addition, briefly explain how your final estimate relates to the graph of f(x) = x9. 2. (a) For x - 2 if x < 2, if 2 <3, if x 3, f (x) -2 = find (i) lim f(x), (ii) lim f(x), (iii) lim f(x), and (iv) f(a) for a = 2 and a 3 xat a a (b) Use the limit definition of continuity to determine if f (x) is right-continuous, left-continuous, continuous, or none of these, at the indicated values of a. are shown below. x sin ( ), and h(r) = -|x| 3. The graphs of the functions f (x) = |x|, g(x) - 0.4 0.1 sin / =x 0.1 -0.4 Use the functions f, g, and h, and the Squeeze Theorem to evaluate lim x sin

Do problems 1 and 3 please. Use any entries for the first problem. Thank you.

Answer 1

3J Faom g saaphs of the unctions f,9 and h we observe that, -1201x sin) and xsin(4)<x - 1x1Sin lim -1x lim e sin (L lim Ix Squeeze Theosem) OS lim xsin () so tim