MATH 1110 Midterm: MATH 1110 Cornell Exam Exam 3Solution

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31 Jan 2019
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For example, the line y = 1 intersect the graph in 5 points. (b) [ 2, 0], (1, 2) (c) since limx 1 f (x) = 1 while limx 1 f (x) = 0. 4. They do not agree and hence the limit does not exist. (d) they are at x = 1 and x = 2. (e) at x = 2. 2 (c) limx sin x+1 cos x = 0+1. 4 (a) both the functions g1(x) = x and g2(x) = ln x are continuous functions. Hence so is their product g(x) = g1(x)g2(x) = x ln x. The domain of g1 is the entire real line, while the domain of g2 is the half real line (0, ), hence the domain of g is (0, ). (b) the function h(x) = ex is continuous. Hence h(g(x)) = ex ln x is also continu- ous in x.

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