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# Math 1431 Final Notes Math 1431 (12589) Calculus

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This 23 page Study Guide was uploaded by nickchukwu on Wednesday August 17, 2016. The Study Guide belongs to Math 1431 (12589) Calculus at University of Houston taught by beatrice constance in Fall 2016. Since its upload, it has received 5 views. For similar materials see Calculus 1 in Math at University of Houston.

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Date Created: 08/17/16

5/18/15 Print Test PRINTABLE VERSION Final You scored 33 out of 45 Question 1 Your answer is CORRECT. 3 x − 12 Evaluate the limit: li2 x→2 x − 4 x + 4 a) 3 b) 12 c) 1 3 d) 2 0 e) f) Does not exist. Question 2 Your answer is INCORRECT. Classify the discontinuities (ifany) for the given function::2f(x) = x < 2 x + 2 x ≥ 2 a) removable discontinuity at 2 b) this function is continuous x = 2 c) infinite discontinuity at d) jump discontinuity at= 2 e) none ofthese. https://www.casa.uh.edu/CourseWare2008/Root/Pages/CW/Users/Student/Grades/PrintTest.htm 1/11 5/18/15 Print Test Question 3 Your answer is CORRECT. 1 Given f(x) = , which ofthe following expressions willrepresent the first step when finding f ' (x) 6 x + 2 using the definition ofderivative? 1 1 ( ) − ( ) 6 (x + h) + 2 6 x + 2 a) lim x→h h ( 1 ) − ( 1 ) 6 (x + h) + 2 6 x + 2 b) lim h→0 h 1 6 (x + h) + 2 c) h→0 h 1 1 ( 6 x + 2+ h) − ( 6 x + 2 d) lim h→0 h ( 1 ) − ( 1 ) 6 (x + h) + 2 6 x + 2 e) h f) none ofthese. Question 4 Your answer is CORRECT. 5 3 Find the derivative of x2x+ 5√x − 3x ′ 5 5 2 a) f (x) = − 4 + − 9x x 2√ x https://www.casa.uh.edu/CourseWare2008/Root/Pages/CW/Users/Student/Grades/PrintTest.2/11 5/18/15 Print Test ′ 5 5 3 b) f (x) = − 3 − − 9x x 2 √x 10 5 c) f (x) = − − − 9x2 x 3 2√ x 10 5 d) f (x) = − + − 9x3 x 3 2 √x f (x) = − 10 + 5 − 9x2 e) x 3 2 √x Question 5 Your answer is INCORRECT. 5π Find f ( ) given f(x) = xcos(3 x). 2 15π a) − 2 b) 1 15π c) 2 d) 3 e) −1 Question 6 Your answer is CORRECT. ′ Suppose f(x) is an invertible differentiable function and f(−4) = −1, f(−1) = 5, f (−4) = −5, f (−1) = 3. Evaluate the derivative ofthe inverse off at − 1. 1 a) 3 − 1 b) 5 https://www.casa.uh.edu/CourseWare2008/Root/Pages/CW/Users/Student/Grades/PrintTest.htm 3/11 5/18/15 Print Test 1 c) 5 −5 d) 5 e) Question 7 Your answer is CORRECT. Differentiate the given function: f(x) = ln 2x − 3 ) 6 x a) f (x) = 2 x − 3 2 ′ 6 x b) f (x) = − 2 x − 3 ′ 6 x2 c) f (x) = 3 2 x − 3 3 x2 d) f (x) = 2 x − 3 1 e) f (x) = 2 x − 3 Question 8 Your answer is CORRECT. 7 Use the graph off(x) below to determine ∫ f(x)dx: 0 https://www.casa.uh.edu/CourseWare2008/Root/Pages/CW/Users/Student/Grades/PrintTest.htm 4/11 5/18/15 Print Test a) 13 b) 2 c) 4 d) 10 e) 0 Question 9 Your answer is CORRECT. ′ The graph of f (x) is shown below. Give the interval(s) where the graph of f(x) is decreasing. https://www.casa.uh.edu/CourseWare2008/Root/Pages/CW/Users/Student/Grades/PrintTest.htm 5/11 5/18/15 Print Test 1 1 a) ( − , ) 2 2 b) (−∞,−1) and (0,1) c) (−1,0) and (1,∞) d) (0,∞) ( −∞,− 1 ) and ( 1,∞ ) e) 2 2 Question 10 Your answer is CORRECT. Find the absolute maximumvalue ofthe function f(x) = x − 2x − 2 on the interval[−3,3]. a) 15 b) 17 https://www.casa.uh.edu/CourseWare2008/Root/Pages/CW/Users/Student/Grades/PrintTest.htm6/11 5/18/15 Print Test c) 13 d) 12 e) 16 Question 11 Your answer is INCORRECT. −− Use differentials to estimate the value of √97 . a) 203 20 197 b) 20 97 c) 10 d) 103 10 10 e) Question 12 Your answer is INCORRECT. Find the slope ofthe tangent line to the curve 2x − 4 xy − 2y = −28 at the point (−1,−3). 1 a) 4 1 b) 2 − 1 c) 4 1 d) − 2 e) undefined https://www.casa.uh.edu/CourseWare2008/Root/Pages/CW/Users/Student/Grades/PrintTest.htm 7/11 5/18/15 Print Test Question 13 Your answer is CORRECT. 2 x d 1 Find dx (∫ −1 t − 3 dt) a) 4 x 2 2 x + 1 b) 8 x − 12 1 c) 2 x − 3 1 d) 4 x − 3 4 x e) 2 2 x − 3 Question 14 Your answer is CORRECT. Compute: ∫ 3 sinh(4 x)dx − 3 cosh(4x) + C a) 4 b) 12 sinh(4x) + C −3 cosh(4x) + C c) 3 d) cosh(4x) + C 4 e) 3 cosh(4x) + C Question 15 Your answer is CORRECT. 1 3 2 Given that f(x) = x − x + 4x − 2 determine the value(s) ofx for which the graph off has a point 6 ofinflection. https://www.casa.uh.edu/CourseWare2008/Root/Pages/CW/Users/Student/Grades/PrintTest.htm 8/11 5/18/15 Print Test a) 2 b) 4 c) −2 d) 3 e) f has no points of inflection Question 16 Your answer is CORRECT. This is a written question, worth 8 points. DO NOT place the problemcode on the answersheet. A proctorwill fill this out afterexamsubmission. Showall steps (work) on youranswersheet forfull credit. ProblemCode:1626 A particle is moving along the hyperbola xy = 8. As it reaches the point (4, 2), the y-coordinate is decreasing at a rate of3 cm/s. At what rate is the x-coordinate ofthe point changing at that instant? a) I have placed my work and my answer on my answer sheet. b) I want to have points deducted frommy test for not working this problem. Question 17 Your answer is CORRECT. This is a written question, worth 8 points. DO NOT place the problemcode on the answersheet. A proctorwill fill this out afterexamsubmission. Showall steps (work) on youranswersheet forfull credit. ProblemCode:1745 π 2 2 Evaluate:∫ 2 cos(3 x)sin (3 x)dx 0 a) I have placed my work and my answer on my answer sheet. b) I want to have points deducted frommy test for not working this problem. https://www.casa.uh.edu/CourseWare2008/Root/Pages/CW/Users/Student/Grades/PrintTest.htm 9/11 5/18/15 Print Test Question 18 Your answer is CORRECT. This is a written question, worth 8 points. DO NOT place the problemcode on the answersheet. A proctorwill fill this out afterexamsubmission. Showall steps (work) on youranswersheet forfull credit. ProblemCode:1885 sin x Find the derivative of y = (7 x + 2) a) I have placed my work and my answer on my answer sheet. b) I want to have points deducted frommy test for not working this problem. Question 19 Your answer is CORRECT. This is a written question, worth 16 points. DO NOT place the problemcode on the answersheet. A proctorwill fill this out afterexamsubmission. Showall steps (work) on youranswersheet for full credit. ProblemCode:1922 Calculate: x (a)∫ 2 dx 4 + x 5 (b)∫ −−−−−2 dx √1 − x 2 (c)∫ ( 2 sin(2x) + sec (x) dx 2x 1 (d)∫ ( e + x ) dx a) I have placed my work and my answer on my answer sheet. b) I want to have points deducted frommy test for not working this problem. Question 20 Your answer is CORRECT. This is a written question, worth 15 points. DO NOT place the problemcode on the answersheet. https://www.casa.uh.edu/CourseWare2008/Root/Pages/CW/Users/Student/Grades/PrintTest.htm 10/11 5/18/15 Print Test A proctorwill fill this out afterexamsubmission. Showall steps (work) on youranswersheet for full credit. ProblemCode:2026 dy Find dx for each ofthe following: (a) y = e2 x+ 42 x (b) y = sec(6 x) + tan x2) (c) y = arcsin(x) + arctan(2 x) −−−− −−−− (d) y = √1 + sin(x) 2 (e) y = 2x cos(4 x) a) I have placed my work and my answer on my answer sheet. b) I want to have points deducted frommy test for not working this problem. https://www.casa.uh.edu/CourseWare2008/Root/Pages/CW/Users/Student/Grades/PrintTest.htm 11/11 PRINTABLE VERSION Final You scored 56 out of 60 Question 1 Your answer is CORRECT. Evaluate the limit: a) b) c) d) e) f) Does not exist. Question 2 Your answer is CORRECT. Classify the discontinuities (if any) for the given function:: a) jump discontinuity at b) this function is continuous c) removable discontinuity at d) infinite discontinuity at e) none of these. Question 3 Your answer is CORRECT. Given , which of the following expressions will represent the first step when finding f ' (x) using the definition of derivative? a) b) c) d) e) f) none of these. Question 4 Your answer is CORRECT. Find the derivative of a) b) c) d) e) Question 5 Your answer is CORRECT. Find . a) b) c) d) e) Question 6 Your answer is CORRECT. Suppose is an invertible differentiable function and the graph opasses through the points and . The slope of the tangent line to the graph of . Evaluate the derivative of the inverse of . a) b) c) d) e) Question 7 Your answer is CORRECT. Differentiate the given function: a) b) c) d) e) Question 8 Your answer is INCORRECT. Use the graph of below to determine : a) b) c) d) e) Question 9 Your answer is CORRECT. The graph of is shown below. Give the interval(s) where the graph of is decreasing. a) b) c) d) e) Question 10 Your answer is CORRECT. Find the absolute maximum value of the function on the interval . a) b) c) d) e) Question 11 Your answer is CORRECT. Use differentials to estimate the value of . a) b) c) d) e) Question 12 Your answer is CORRECT. Find the slope of the tangent line to the curve at the point . a) b) c) d) e) undefined Question 13 Your answer is CORRECT. Find a) b) c) d) e) Question 14 Your answer is CORRECT. Compute: a) b) c) d) e) Question 15 Your answer is CORRECT. Given that determine the value(s) of for which the graph of has a point of inflection. a) b) c) d) e) f has no points of inflection Question 16 Your answer is CORRECT. This is a written question, worth 8 points. DO NOT place the problem code on the answer sheet. A proctor will fill this out after exam submission. Show all steps (work) on your answer sheet for full credit. Problem Code: 1663 A cylindrical tank with a radius of 5 m is being filled with water at a rate of 2 m /min. How fast is the height of the water increasing? a) I have placed my work and my answer on my answer sheet. b) I want to have points deducted from my test for not working this problem. Question 17 Your answer is CORRECT. This is a written question, worth 8 points. DO NOT place the problem code on the answer sheet. A proctor will fill this out after exam submission. Show all steps (work) on your answer sheet for full credit. Problem Code: 1761 Evaluate: a) I have placed my work and my answer on my answer sheet. b) I want to have points deducted from my test for not working this problem. Question 18 Your answer is CORRECT. This is a written question, worth 8 points. DO NOT place the problem code on the answer sheet. A proctor will fill this out after exam submission. Show all steps (work) on your answer sheet for full credit. Problem Code: 1876 Find the derivative of a) I have placed my work and my answer on my answer sheet. b) I want to have points deducted from my test for not working this problem. Question 19 Your answer is CORRECT. This is a written question, worth 8 points. DO NOT place the problem code on the answer sheet. A proctor will fill this out after exam submission. Show all steps (work) on your answer sheet for full credit. Problem Code: 1943 Calculate: (a) (b) (c) (d) a) I have placed my work and my answer on my answer sheet. b) I want to have points deducted from my test for not working this problem. Question 20 Your answer is CORRECT. This is a written question, worth 8 points. DO NOT place the problem code on the answer sheet. A proctor will fill this out after exam submission. Show all steps (work) on your answer sheet for full credit. Problem Code: 2084 Find for each of the following: (a) (b) (c) (d) a) I have placed my work and my answer on my answer sheet. b) I want to have points deducted from my test for not working this problem.

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