Chapter 2.1, Problem 35E

Exercise To Try 3 Determine the limits lim 2-a X→1 (x–1)2

Help how do I find the limits?

find the limit or explain why it does not exist

In Exercises 79-86, find each limit. Use TABLE and start with ATbl = 0.1. Then use 0.01, 0.001, and 0.0001. When you think you know the limit, graph and use TRACE to verify your assertion. Then try to verify it algebraically. Vx - 1 a - 4 79. lim 1 x - 80. lim a2 Va? + 5- 3 + 5 - 3 V4 + x - V4 - x V3 - x - V3 82. lim 81. lim V7 + 2x – V7 x - Vx 83. lim 84. lim x1 x - 1 7 - V49 2 - Vx 85. lim 86. lim x4 4 - x

In Exercises 43-46, use formulas (3)–(5) to evaluate the limit. 44. lim N → ∞ N =

Compute and write a sentence explaining how you computed the limits. (seen in attached image)

1. Evaluate the limit and justify each step by indicating the appropriate Limit Laws. Do NOT use Direct Substitution Property. 3x? lim x+2 Vx + 14

Do not forget, limits at infinity are different from limits that might go to infinity! Evaluate the limit. 6 lim x →7 x 7 -

In Exercises 87-89, use GRAPH and TRACE to find each limit. When necessary, state that the limit does not exist. x - 5 x2 - 4x - 5 find lim f(x) and lim f(x). 89. For f(x) X-1 Sx² – 2, for x < 0, 12 - x², for x 2 0, find lim f(x) and lim f(x). 87. For f(x) = Answers to Quick Checks X-2 1. (a) f(3) does not exist; (b) 6 2. (a) 1, 7, does not exist; (b) 3 3. (a) 3; (b) 3; (c) 3 4. (a) Limit does 20x2 88. For g(x) x + 2x2 + 5x find lim g(x) and lim g(x). not exist; (b) 5; (c) 6