Suppose that f : D → R and that c is an accumulation point of D. Prove that if limx→c f(x) = L, then limx→c af(x) = aL for any real number a. Prove by cases.

ff is continuous and ƒ(5) = 2 and ƒ(4) = 3 then lim ƒ(4x² — 11) = 2. x→2 True False

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.

Use the limit definition of the derivative to determine ƒ '(2) if ni=xso enil ls1 gribnoqasnos erli B10 f(x) = x-1 ¹ f '(c) = lim f(x)-f(c) X-C X-C

Assume that rs f(x) < 3r. Compute lim f (x)

3. Find the limits. (Be sure 3x lim a-1 x→2 V4x+1-1

Use the La`Hospital rule to evaluate

Suppose f: (0, ∞) → (0, ∞) is a function such that lim f(x) exists x→0 and equals 4. True or false: lim √f(x) exists and equals 2. x→0 True False

Part. c. True or False: lim x →→∞0 2x 3e +5e -X 2x -X e -e = 5.

Show that lim (Vx² +1 – x) = 0. Hint: Observe that 1 Vx² + 1 – x = Vx2 +1 + x