MATH 1100Y Final: MATH1101Y-Final-Solutions (2)

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31 Jan 2019
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Mathematics 1101y calculus i: functions and calculus of one variable. Instructions: do parts u, v, and w, and, if you wish, part b. Show all your work and justify all your answers. Do all four (4) of 1 4. neurons): compute dy dx as best you can in any three (3) of a f. Solution to a. ln(x + y) = 1 x + y = 0 y = x, so. Using the product rule, dy dx d dx ( x) = 1. (cid:4) dy dx d dx (x arctan(x)) = = 1 arctan(x) + x dx dx arctan(x) + x . 1 + x2 = arctan(x) + d dx. Solution to c. using the chain and power rules, dy dx d dx. Solution to d. d dx sin(cid:0)x2(cid:1) = cos(cid:0)x2(cid:1) dt(cid:0)t2 1(cid:1) d dt (2t + 1) dy dt dx dt dy dx d x2 = cos(cid:0)x2(cid:1) 2x = 2x cos(cid:0)x2(cid:1) . (cid:4)

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