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MATH 152 -
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MATH152, 501–506, Spring 2011, Answers for the sample problems for the Final1.132.38π153. (a)15π2; (b)67π64.π125. 0.3125(J)6.49π √24+ 1!7. (a) 2 −5e(b)x8−132sin 4x + C(c) −14cos 2x −18cos 4x + C(d)sec3x3+ C(e)52arcsin x −15x√5 − x2+ C(f) −1x− arctan x + C(g) −ln23(h) 48. 149.π81(145√145 − 1)10. 2π11. ∞12. (a) divergent(b) convergent but not absolutely convergent1(c) absolutely convergent(d) convergent13. radius of convergence R =12; interval of convergence−52,7214. e3∞Xn=0(x − 3)nn!15.∞Xn=0x2n+222n+1(2n + 1)!16. (x − 1)2+ (y − 2)2+ (z − 32) = 3017. (a) θ = arccos10√290(b) proj~a~b =< −2029,3029,4029>; comp~a~b =10√29(c) ~a ×~b =< 9, 10, −3 >.18.
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