Test 1 Review.pdf - Math 1309 Chapter 10.1-5,7 Test 1...

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Math 1309 Chapter 10.1-5,7 Test 1 Review 1. Page 500 #59-66,73-80 Page 512 #25-32. Find the limit, if it exists. a. lim 𝑥→−2 √5𝑥 + 2 3 b. lim 𝑥→0 2𝑥 2 −3𝑥 𝑥 c. lim 𝑥→0 √𝑥+2 −√2 𝑥 d. lim 𝑥→∞ 4𝑥 2 −1 𝑥+2 e. lim 𝑥→−∞ 2𝑥 2 +3𝑥+1 𝑥 4 −𝑥 2 2. Page 512 #51-64 Page 524 #69-74. a. Use limits to determine horizontal and vertical asymptotes. ?(𝑥) = 𝑥+5 𝑥 2 ?(𝑥) = 3𝑥−1 2𝑥+4 b. Determine if the function is continuous. ?(𝑥) = { 𝑥 + 5 𝑥 ≤ 0 −𝑥 2 + 5 𝑥 > 0 ?(𝑥) = { 1 − 𝑥 𝑥 < 1 2𝑥 + 3 𝑥 ≥ 1 3. Page 538 #19-42. Use the limit definition to find the first derivative. a. ?(𝑥) = 𝑥 2 + 3𝑥 − 1 b. ?(𝑥) = √𝑥 + 3 c. ?(𝑥) = 1 𝑥+2 4. Page 547 #33-56, 77-82 Page 670 #1-30. Use the derivative rules to find ? (𝑥) a. ?(𝑥) = − 2 𝑥 3 + 3 𝑥 − 3𝑥 3 b. ?(𝑥) = √𝑥 + 4 √𝑥 3 + 2 c. ?(𝑥) = (3𝑥 − 4) 2 d. ?(𝑥) = 2𝑥 5 −4𝑥 3 +2𝑥 𝑥 3 e. ?(𝑥) = (2𝑥 + 5)(𝑥 2 − 𝑥) 5. Page 548 #57-60. Tangent line problems.
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