Mathematics 1225A/B Final: Final1.pdf

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If f (x) = ln(x3 + 2x), nd f (1). If f (x) = log3 x, nd f (5). + c d: x2 + 1 + c e: x2. 2 e3x z e3xdx e: none of a,b,c,d. If f (x) = z 2xe2xdx and f (0) = 1, nd f (ln 2). Find the area under the curve y = x2 on the interval [1, 3]. 1 (x2 3x 4)dx b: z 1 (x2 3x 4)dx e: z 4. 4 (x2 3x 4)dx c: z 1 (3x + 4 x2)dx. Find the volume generated when the region bounded by y = x, y = 0 and x = 4 is rotated about the x-axis. 3 dy y based on a 2007 exam. If f (x, y) = x3y 2xy2, nd fyy(x, y). A: (0, 0) is not a critical point of f . B: f has a local maximim at (0, 0).

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