Section 2.1 Homework

4. This is similar to Section 2.1 Problem 38: The function G is represented by the formula G(x)={−5 x+(6)if x≤ 2, −4 x + (3)if x>2. Find the following limits. If the limit does not exist, use ``DNE''. 1) lim G(x) x → 2− Answer: 2) lim G(x) x → 2+ Answer: lim G(x) x → 2 Answer:

1) -4 🔑 -4 2) -5 🔑 -5 3) DNE 🔑 DNE

1. This is Section 2.1 Problem 1 to 10: The function G is represented by the graph in the textbook. Use the graph to find the following limits. If the limit does not exist, use "DNE". 1) lim G(x) x −1− Answer: 2) lim G(x) x → −1+ Answer: 3) lim G(x) x → −1 Answer: 4) lim G(x) x → 0− Answer: 5) lim G(x) x → 0+ Answer: 6) lim G(x) x → 0 Answer: 7) lim G(x) x → 1− Answer: 8) lim G(x) x → 1+ Answer: 9) lim G(x) x → 1 Answer: 10) lim G(x) x → 3 Answer:

1) 1 🔑 1 2) -1 🔑 -1 3) DNE 🔑 DNE 4) -1 🔑 -1 5) -1 🔑 -1 6) -1 🔑 -1 7) -1 🔑 -1 8) -1 🔑 -1 9) -1 🔑 -1 10) 0 🔑 0

5. This is similar to Section 2.1 Problem 44: The function g is represented by the formula g(x)=x2−1/x−1 Find the following limits. If the limit does not exist, use "DNE". 1) lim g(x) x → 0 Answer: 2) lim g(x) x → 1 Answer:

1) 1 🔑 1 2) 2 🔑 2

3. This is Section 2.1 Problem 50: The function H is represented by the formula H(x)={ 2if x≤ −1, 3x if x>−1. Find the following limits. If the limit does not exist, use "DNE". 1) lim H(x) x → −1− Answer: 2) lim H(x) x → −1+ Answer: 3) lim H(x) x → −1 Answer:

1) 2 🔑 2 2) -3 🔑 -3 3) DNE 🔑 DNE

7. This is similar to Section 2.1 Problem 56: The function s is represented by the formula s(x)=6/x+1 Use numerical tables to find the following limits. If the limit does not exist, use "DNE". 1) lim s(x) x → −1 Answer: 2) lim s(x) x → ∞ Answer:

1) DNE 🔑 DNE 2) 0 🔑 0

6. This is similar to Section 2.1 Problem 55: The function s is represented by the formula s(x)=2/(x+2)^2 +(−1) Use numerical tables to find the following limits. If the limit does not exist, use "DNE". Use "infty" for ∞ 1) lim s(x) x → −2 Answer: 2) lim s(x) x → ∞ Answer:

1) infty 🔑 infty 2) -1 🔑 -1

2. This is Section 2.1 Problem 21 to 30: The function T is represented by the graph in the textbook. Use the graph to find the following limits. If the limit does not exist, use ``DNE''. Use "infty" for ∞. 1) lim T(x) x → −3− Answer: 2) lim T(x) x → −3+ Answer: 3) lim T(x) x → −3 Answer: 4) lim T(x) x → 0− Answer: 5) lim T(x) x → 0+ Answer: 6) lim T(x) x → 0 Answer: 7) lim T(x) x → −1− Answer: 8) lim T(x) x → −1+ Answer: 9) lim T(x) x → −1 Answer: 10) lim T(x) x → ∞ Answer:

1) infty 🔑 ∞ 2) −infty 🔑 −∞ 3) DNE 🔑 DNE 4) infty 🔑 ∞ 5) infty 🔑 ∞ 6) infty 🔑 ∞ 7) 0 🔑 0 8) 0 🔑 0 9) 0 🔑 0 10) 1 🔑 1

8. Use the given graph of f to state the value of each quantity, if it exists. (If an answer does not exist, enter DNE.) (a) lim f(x) x→3− (b) lim f(x) x→3+ (c) lim f(x) x→3 (d) lim f(x) x→7 (e) f(7)

a) 2 🔑 2 b) 5 🔑 5 c) DNE 🔑 DNE d) 6 🔑 6 e) DNE 🔑 DNE