MAC 2311 Midterm: MAC2311 S10 Test 4
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Calculus 1 page 3 (4) (16 points) for the function f (x) = x4(15 x2) = 15x4. X6, nd the fol- lowing. (a) the intervals of increase or decrease. (b) the intervals of concavity. (c) the local extrema. Classify each as a maximum or minimum. (d) the in ection points. (e) sketch the graph of y = f (x) Calculus 1 page 4 (5) (10 points) for the function f (x) = 2x x2, evaluate the integral. 0 f (x) dx using a limit of riemann sums: 2(cid:1) sin x (8) (8 points) find the equation of the tangent line to the curve at the point (2, 3). x2 + xy y2 = 1. Calculus 1 page 6 (9) (50 points) integrate the following. (a) z (cid:18)5 + 3 x3 + 4 sin x(cid:19) dx (b) z (cid:18) 2 x. 1 + x2(cid:19) dx (c) z x2(cid:0)3 + x3(cid:1) 4 dx (d) z 1.
