MATH10560 Midterm: Math10560MockExam1ASp16Sols copy 3
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2. (a) (a) (b) (b) (c) (c) (d) (d) (e) (e) 4. (a) (a) (b) (b) (c) (c) (d) (d) (e) (e) 6. (a) (a) (b) (b) (c) (c) (d) (d) (e) (e) Multiple choice f (x) = x3 + x + ln(x) 1. (6 pts) the function is a one-to-one function (there is no need to check this). The function f (x) = x3 + x + ln(x) is one-to-one (there is no need to check this). By guess and check we notice that f (1) = 2 so f 1(2) = 1. 2. (6 pts) find the derivative of the function f (x) = (x2 1)5(x2 + x + 1)2. Notice that ln(f (x)) = 5 ln(x2 1) + 2 ln(x2 + x + 1) . Di erentiating both sides with respect to x we have. 10x x2 1 x x2 + 1 f (x) = (x2 1)5(x2 + x + 1)2.
