MATH 1013 Final: MATH1013 Past Final Exams
31 Jan 2019
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No aid (e. g. calculator, written notes) is allowed. Evaluate exact values of the following quantities, if they exist. If any does not exist, state so. (in radians) sin. If the limit does not exist clearly explain why not. (i) (iii) lim x 0 lim x 3 cos x 1 (tan x) 2 x 3. | x 3 | (ii) lim x 9 (iv) lim x . 3 x x 2 + 2 x x 2 + 2 x + 1. Therefore the intermediate value theorem assures us that there must be at least one value of c between -1 and 1, such that f(c)=0. If you believe that the mean value theorem applies to f(x) on the interval [1,2], find one value of x between 1 and 2 that satisfies the theorem. If you believe that the theorem does not apply, explain why not. [sin2 (tan 2t)] (ii) d dx (ln(4e2x ))
