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Animals - Calculus - Exam

Exams, Calculus

Post: March 16th, 2013
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Key points of this exam are: Animals, Multiplying Constant, Function, Present, Integrand, Decreasing, Concave Up, Quantities, Ascending Order, Rate of Change
Key points of this exam are: Animals, Multiplying Constant, Function, Present, Integrand, Decreasing, Concave Up, Quantities, Ascending Order, Rate of Change
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Contents
Math 106: Review for Exam I 1. Find the following. [Substitution tip: usually let u = a function that’s “inside” another function, especially if du (possibly off by a multiplying constant) is also present in the integrand.] 4 (a) 1 ex √ dx x √ 2π (b) π cos7 (5x) sin(5x) dx (c) 7x2 dx 1 + x6 10 (d) 6 √ x 10 − x dx 2. Suppose f (x) is decreasing and concave up. (a) Put the following quantities in ascending order. b L100 , R100 , T100 , M100 , a f (x) dx (b) What can you say with certainty about where S200 would fit into your list above? 3. Suppose f (t) is the rate of change (in animals per month) of a population P (t). 12 (a) What does 4 f (t) dt represent in this problem? 12 (b) Find the best possible left, right, midpoint, trapezoidal, and Simpson’s approximations to 4 f (t) dt given the data in the table below. t f (t) 4 15 6 11 8 8 10 4 12 3 7 4. Find bounds for each of the following errors if I = 2 ln x dx. (a) |I − L100 | (b) |I ..

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