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This is the Exam of Calculus which includes Constant, Constant Height, Concave Up, Antiderivative, Compare, Natural Domain, Average, Range, Natural Domain etc. Key important points are: Confirm, Antiderivative, Function, Mathematical Notation, Clearly and Legibly, Necessary Steps, Limits, Reference Triangle, Rewrite, Trigonometric Functions
Typology: Exams
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Name: Show all work, clearly and legibly, to receive full credit.your solution, and proper use of mathematical notation all count. You may use a calculator, Correct spelling, organization of but no notes, books, or other resources. Good luck! 1.) (10 pts.) Compute an antiderivative, F (x), of the function f (x) = (^) exe (^) + sinx^ + cos x +x^ + 2x (^2) + 4x and check your result to confirm that F ′(x) = f (x).
2.) (15 pts.) Compute the following limits. Be sure to show all necessary steps. a.) (8 pts.) lim x→ 0 3 exx^ −+ 2^7
b.) (7 pts.) (^) xlim→∞^ cosx^ x
4.) (15 pts.) Compute the following derivatives. Do not simplify your results. a.) (5 pts.) f (x) = eπxe
b.) (5 pts.) g(x) = log 7 (tan(x^2 ))
c.) (5 pts.) h(x) = sin(cot x (^2) ln x^ x)
5.) (15 pts.) Use the table of values x 2 f ( 1 x ) g( 3 x ) f ′( 4 x ) g−′(x 1 ) 3 − 4 5 − 2 2 to compute the following. a.) (5 pts.) h ′(2), for h(x) = f (g(x))
b.) (5 pts.) j ′(3), for j(x) = f (x)g(x)
c.) (5 pts.) k ′(2), for k(x) = f g^ ((xx))
7.) (15 pts.) An advertisement consists of a rectangular printed region plus 1-inch marginson the sides and 2-inch margins at top and bottom. If the area of the printed region is to be 92 square inches, use calculus to find the dimensions of the printed region and overalladvertisement that minimize the total area. Be sure to confirm that you have minimized the total area. Your answers should be exact answers, not decimal approximations.
