1100 Math (calculus techneqnies) Final Exam Fall 2020 PDF

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It is the final exam in the class so that students can make sure they know everything that has been on past test....

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MATH1100 - Final Exam Paper Portion Spring2021

Instructor:

Hannah Lewis

A# Student Name (print): This portion of the exam contains 5 pages (including this cover page) and 4 questions. Enter your answers in the space provided. Draw a box around your final answer. Complete your solutions to the “show your work” problems on the page indicated. • Organize your work, in a reasonably neat and coherent way, in the space provided. Work scattered all over the page without a clear ordering cannot be assessed accurately. • Mysterious or unsupported answers will not receive adequate feedback. A correct answer, unsupported by calculations, explanation, or algebraic work doesn’t show achievement of the objective; an incorrect answer supported by substantially correct calculations and explanations may show partial achievement of the objective. • Provide exact answers unless otherwise instructed. • Simplify all answers as much as possible. This means that you need to need to combine like terms, reduce fractions, etc. (You do not need to rationalize denominators.) • Be sure to state units for applied problems. • Clearly identify your answer for each problem. • Justify every step of your work for full credit. • Any questions left blank will not be eligible for exam retakes. • Sign here indicating that you have not used material outside of your attached note page, desmos.com, and/or your calculator to complete this exam.

MATH1100 - Final Exam Paper Portion

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Show your work. Clearly identify your answer. Justify every step. 1. (10 points) Find the equation in point-slope form of the tangent line to the graph of f (x) = x3 + 3 − ln x at the point (1, 4).

MATH1100 - Final Exam Paper Portion

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2. (10 points) Do any one and ONLY one of the following two problems. Cross out completely the problem that is NOT to be graded. Clearly indicate how you use the methods of calculus to obtain the results. 2A. Some years ago it was estimated that the demand for steel approximately satisfied the equation p = 168 − 15x, and the total cost of producing x units of steel was C(x) = 146 + 48x. (The quantity x was measured in millions of tons and the price and total cost were measured in millions of dollars.) Determine the level of production and the corresponding price that maximize the profits. (Hint: Profit = Revenue − Cost and R = xp.) 2B. The monthly advertising √ revenue A and the monthly circulation x of a magazine are related approximately by the equation A = 3 x2 − 256 for x ≥ 16, where A is given in thousands of dollars and x is measured in thousands of copies sold. At what rate is the advertising revenue changing if the current circulation is x = 20 thousand copies and the circulation is growing at the rate of 1 thousand copies per month? (It is = 1.) a related rates problem asking you for the value of dA when x = 20 and dx dt dt

MATH1100 - Final Exam Paper Portion

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3. (10 points) Do any one and ONLY one of the following two problems. Cross out completely the problem that is NOT to be graded. Clearly indicate how you use the methods of calculus to obtain the results. 3A. The rate of growth of a certain cell culture is proportional to its size. In 10 hours a population of 1 million cells grew to 4 million. How large will the cell culture be after 20 hours? Simplify your final answer to a whole number. 3B. 3 x2 − 2x + 10 dollars, where x denotes the number of A company’s marginal cost function is C ′ (x) = 10 units produced in 1 day. Determine the increase in cost if the production level is raised from x = 1 to x = 4 units. Simplify your answer.

MATH1100 - Final Exam Paper Portion

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4. (10 points) Find all points (x, y) where f (x, y) = x3 − y2 − 3x + 4y has a possible relative maximum or minimum. Then, use the second-derivative test to determine, if possible, the nature of f (x, y) at each of these points. If the second-derivative test is inconclusive, so state. (Make sure to include all necessary steps.)...