Chapter 9.3, Problem 45E

(iii) lim x → 0 √16+ x - √16 X

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

f(x) Suppose f(x)→- 200 and g(x)→0 with g(x) < 0 as x→3. Determine lim x→3 g(x) f(x) lim ..... (Simplify your answer.) X→3 9(x)

f(x) 80. If lim x→-2 x? 1, find f(x) b. lim x2 (x) х

p(x) Suppose that p(x) and q(x) are polynomials. The expression lim I-a g(1) P(z) = L means that as a gets very close to a -- without being a, the output q(z) gets very close to L. How to find L? • If q(a) + 0, then L = p(a) That's simply the evaluation of the function at a. q(a) • If p(a) = 0 and g(a) = 0, then p(x) and g(z) have a common factor. Factor both polynomials and cancel the common factors out. Then L is the limit of the equivalent function. • If p(a) + 0 and g(a) = 0, find the one-sided limits and compare them. Practice 2² + 4x + 4 1. f(x) = f(2) = lim 2² – 4r + 4 f(z) = x² + 2x 72 - 27 lim f(x) = 2. f(x) = f(2) = I-2 1² + 4x + 4 3. f(x) = f(2) = lim 12 – 4 (x) =/ 72 f(x) = 4x + 4 f(2) = lim f(æ) 4. = x² – 4 x? – 4 5. f(x) = 12 – 2x f(2) lim f(x) =

2x2 + x + 7 if x -2 (a) Find lim f(x). x--2- (b) Find lim f(x). x→-2+ (c) Find lim f(x), or show that it does not exist. x--2 (d) Is f continuous at x =-2? Justify your answer.

x+2 2. Consider the function f (x) |a+2] Does lim f (x) exist? Give reasons for your conclusion. x-2

Is there any better explanation on how on answering the function?

Find lim,-2 f(x) -3 -2 2 lim,-2 f(x) = 0 O lim,→-2 f(x) = 2 O lim,-2 f(x) = 1 O Does Not exist 2.