Homework 10 - MATH 106 CALCULUS I FOR BIO& SOC SCI FALL 2011 ´ ´ INSTRUCTOR JOSE MANUEL GOMEZ Homework 10 Due date Friday December 2 2011

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Unformatted text preview: MATH 106 CALCULUS I FOR BIO. & SOC. SCI. FALL 2011 ´ ´ INSTRUCTOR: JOSE MANUEL GOMEZ Homework 10. Due date Friday December 2, 2011 Please show all your work. (1) (6 Points) Find the most general antiderivative of the following functions: 2 (a) (2 Points) f (x) = x3 + 3 . x √ √ √ (b) (2 Points) g (x) = x + 3 x + 4 x. (c) (2 Points) h(x) = sec2 (2x). (2) (6 Points) Compute the following integrals: (a) (3 Points) 2 dx. x e−3x + (b) (3 Points) 1 0 1 1 + x2 dx. (3) (4 Points) Solve the following initial value problem. dy = sin(πt) + t, with y (0) = 2. dt (4) (8 Points) Find the following quantities: (a) (3 Points) Find the area under the graph of f (x) = x + √ x, for 1 ≤ x ≤ 2. (b) (5 Points) Find the area of the region bounded by the curves y = 4 − x2 and y = x2 . (5) (6 Points ) Find the derivative of the following functions. (a) (3 Points) x2 F (x) = √ 2 + tdt 0 (b) (3 Points) ex ln(t)dt. G(x) = 1 1 ...
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This note was uploaded on 01/20/2012 for the course CALC AS.110.106 taught by Professor Josegomez during the Fall '11 term at Johns Hopkins.

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