Express the integrand as a sum of partial fractions and evaluate the integral.

A. tan-1  -  -  + C
B. tan-1  + ln  -  + C
C. tan-1  +  -  + C
D. tan-1   -  +  + C

Answer: C

Mathematics

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Rotate the coordinate axes to change the given equation into an equation which has no cross product (xy) term. Identify the graph of the equation as a hyperbola, ellipse, parabola, a straight line, or parallel lines.3x2 - 2xy + y2  - 3x + 7y = 0

A. 4u2 + 2u + 8v = 0; Parabola
B. 4v2 + 8v = 0; Parallel lines
C. -u2 + 4v2 + 2u + 8v = 0; Hyperbola
D. u2 + 4v2 + 2u + 8v = 0; Ellipse

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Mathematics

Find the indicated number of terms of the Maclaurin polynomial for f(x) and use it to approximate the function value.f(x) = sin x; f(8°); 3 terms

A. 0.8696677 B. 0.1391731 C. 0.1298944 D. 0.1400805

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Mathematics

Using Green's Theorem, compute the counterclockwise circulation of F around the closed curve C.F = - i + j; C is the region defined by the polar coordinate inequalities 6 ? r ? 10 and 

A. 0 B. 128 C. 136 D. 40

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Mathematics

Find the formula and limit as requested.For the function f(x) = 9 - 3x2 , find a formula for the lower sum obtained by dividing the interval [0, 1] into n equal subintervals. Then take the limit as n?? to calculate the area under the curve over [0, 1].

A. ; Area = 1
B. 9 - ; Area = 8
C. 9 + ; Area = 10
D. 9 - ; Area = 8

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Mathematics