Chapter 2.2, Problem 2E

1. Part 1 - Application 30 1+ 23-x Let f(x) = a. Use tables and graphs to find lim f(x) and lim f(x). 00x3 ∞0-x b. Identify any horizontal asymptotes. c. What is the y-intercept? d. How is the numerator of the fraction for f related to part b? e. Sketch the graph.

c) lim f(x) x-1 2x - 1 if x 2 a) lim f(x) x→2- b) lim f(x) x→2+ c) lim f(x) X-2 3. Sketch the graph of a function that satisfies the following conditions: f(3) = 1 ; lim f(x) = -3; lim f(x) = 0: lim f(x) DNE %3D x-3- x-3+ x-3 Section 2.3: Evaluate the following limits. MacBook Air 吕0 DII O00 F3 F4 F5 F6 F7 F8 F9

Instructions as number 1:  Please sketch the graph of f and evaluate each. Use appropriate superscripts.

Use the graph of the function f shown below to respond to each prompt. The first prompt is worth 3 points. The other prompts are worth 0.5 points each: 10-9-8--6-5-4-3-2 ● Does Not Exist Undefined x→-3 lim x-3 . Can be found, lim f(x) lim x → 1 Does Not Exist Undefined f(x) = lim f(x) x →1 . Can be found, f(x) = The function has several discontinuities. State the location of two discontinuities and explain, using the definition of continuity, why the function is not continuous at that location. Does Not Exist Undefined f(- 6) 10+ 9 Edit Insert Formats B IU X₂ X² A E = = E- 3? e & N lim f(x) x+3+ . Can be found, lim f(x) = x+3+ 8+ f(-3) f(-7) . Can be found, f(-7)= . Can be found, f(-3) = Does Not Exist Undefined 7 6 5 4- 3 2 1 -2 -3 -4 -5 -6 -7 -8 9+ --10+ 2 A I V 4 5 6 7 8 9 10 Does Not Exist Undefined lim x →-3+ 。 Can be found, lim f(x) x → f(x) = - 3+ Does Not Exist Undefined f(1) Can be found, f(1) = Does Not Exist Undefined lim f(x) x →3 . Can be found, f(x) = lim x →3 Does Not…

5X²+1 IF X<\ Let F(X) = {(x-2) IF XZ1 a, Find Limx→ 1¹ and lim x→# f(x) b. does Lim X→1 f(x) exist? C. Sketch the graph of f

Evaluate lim h→0 Answer: f(4+h)-f(4) h where f(x) = 7x + 1.

Consider the follovwing graph of the function g. From the given graph of g, state the numbers at which g is discontinuous. (Enter your answers as a comma-separated list.)

1) Consider the graph of function f(x): Evaluate: (a) lim f(x) x+-2- Ay 5- (b) lim f(x) x-2+ (c) lim f(x) X-2 (d) f(-2) -> (e) Is f continuous at x =-2? Explain. -5 -2-