MATH113 Final: MATH 113 UofA Exam Final1 solution
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3(2x + 1) 2(3x 1) (2x + 1)2. 1 (c) g (x) = g (2) = h (x)x h(x) ( 3)(2) 4 x2. 2 f (x)dx z 5 f (x)dx +z 1 f (x)dx z 5. = 6y + 6x (x3 + y3) = d dx dy. = 2y x2 dx 2x dx dy (y2 2x) = 2y x2 dx dy dx. Since (1 x) 0 as x 1+ and x 1+ x > 1 1 x < 0 we have lim x 1+ lim x 1+ cos( x) 2(1 x)(x 2) (b) lim x . |x|q1 + 10 since x x < 0 |x| = x x x2 ) x2. U2 + 1 (c) let u = x3. T2 + 1 dt = 3x2 d duz u. + 3 = y + x d dx dy dx (1 x) = y 3 d dx dy dx dy dx dy dx dy.
