MAT 182: Calculus II Test on Chapter 6: Applications of Integration Take-Home Portion Points as Assigned for Each Exercise 40 Points Total.

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1 Name: Section: Date: MAT 182: Calculus II Test on Chapter 6: Applications of Integration Take-Home Portion Points as Assigned for Each Exercise 40 Points Total Guidelines 1. Each student must produce his or her own work for all exercises. This is NOT a group project. Failure to produce individual work will result in a grade of zero and possible additional sanctions. 2. Any acts of academic dishonesty will result in a grade of zero and possible additional sanctions. 3. The use of calculators, computer algebra systems, and any other technological aids is prohibited EXCEPT where noted otherwise. However, you may use any resources distributed in class to assist (e.g., formula sheets, class examples, graphs of hyperbolic functions, etc.). 4. All work is to be done in the space provided in this packet. If additional room is needed, you may staple additional sheets to the back of this packet as necessary, but please clearly indicate in the space provided for each such exercise that work is on the attached sheet(s) and submit your supplemental work in order of the exercises as presented in this packet. 5. Completed exercises must be submitted in the order provided in this packet. Each exercise that is not in the correct sequence will earn zero points toward the final quiz grade. 6. All work must be shown for each exercise in order to receive full credit. 7. All exercises are to be completed using only techniques discussed in class. 8. No credit will be given for any exercise to which the submitted work is messy or illegible. 9. This entire packet must be submitted with this cover sheet as the first page of the completed quiz. 10. Completed quizzes must be submitted no later than the beginning of class on the following date: Date Due: Monday, February 19, 2018 Late submissions will not be accepted for any reason and will receive a grade of zero. Grade: / 40

2 Directions: Complete each exercise using only techniques discussed in class. You must show all work and clearly indicate final answers to receive full credit. Unless otherwise specified, give exact values in at least reasonably simplified form. 1. Use L Hôpital s Rule to evaluate the limit below. You must demonstrate when L Hôpital s Rule is to be applied by first showing an appropriate indeterminate form is obtained. Be sure to work with the given hyperbolic functions and use the appropriate graphs, identities, derivatives, and/or other formulas on the handouts distributed in class to assist in your calculations; do NOT rewrite the hyperbolic functions in terms of exponentials. (6 Points) 1 coth x lim x 1 tanh x

3 x f x x. Be sure to work with the given hyperbolic functions csch x and use the appropriate graphs, identities, derivatives, and/or other formulas on the handouts distributed in class to assist in your calculations; do NOT rewrite the hyperbolic functions in terms of exponentials. (6 Points) 2. Compute f x for 2 cosh

4 3. Express the exact value of the integral below in terms of exponential and/or logarithmic functions. Do NOT leave the result in terms of any hyperbolic functions; use the definitions of hyperbolic and inverse hyperbolic functions on the handout distributed in class to rewrite their values in terms of exponential and/or logarithmic functions, respectively, then simplify completely. (8 Points) x dx 25

5 x over the interval 0, ln 1 2. You must evaluate the associated integral using hyperbolic functions directly, but you must then rewrite any resulting hyperbolic functions in terms of exponential functions using the definitions distributed in class in order to compute the exact area desired. (10 Points) 4. Calculate the exact area under f x sech

6 Compute the area of the region bounded by f x x 7 x 12 x 2 and g x 2 4x x. Although a detailed graph is not required, be sure to provide at least a rough sketch that indicates the basic shapes of the functions, the region in question, and the points of intersection. You may use basic concepts from Algebra to obtain all necessary points for a rough sketch (e.g., formula for vertex of a parabola, equating functions to find points of intersection, basic shapes of graphs based on degrees of associated polynomials, etc.). There is no need to incorporate any graphing techniques from Calculus, such as the first or second derivative test, but you may do so if you feel it will help. Please note that any maxima or minima for f are not pretty, but all other necessary points are. (10 Points)

7 Extra Credit: Complete each exercise as directed. You must show all work to receive full credit. (Points as Assigned for Each Exercise) 2 2 x e 1 intersect at the point ln 1 2, by 2 2 substituting the x-value into each function and computing the associated y-value (both functions must produce the same y-value, and it must be the exact y-value given in the problem description in order to verify the point of intersection is correct). You must use the definitions of hyperbolic functions provided in class to rewrite sech x in terms of exponential functions before substituting. (3 Points) 6. Verify that f x sech x and g x

8 2 x e 1, and the y-axis. 2 You may use results from previous exercises in this test packet as desired to expedite the process. (3 Points) 7. Determine the area of the region bounded by f x sech x, g x

KEY Algebra: Unit 10 Graphing Quadratic Equations & other Relations

Name: KEY Algebra: Unit 10 Graphing Quadratic Equations & other Relations Date: Test Bank Part I: Answer all 15 questions in this part. Each correct answer will receive credits. No partial credit will