Question

Need help finding the following functions using the graphs.

Answer 1

1. DNE
2. 3
3. 0
4. 0
5. 1

Explanation:

1. The limit of f+g is the sum of the limits: lim(f)+lim(g). Unfortunately, the limit of g from the left (2) is different from the limit of g from the right (1) at x=1. Hence, the limit of g does not exist, so the limit of f at that point (2) is irrelevant.

2. lim(f+g) = lim(f)+lim(g) = 1 + 2 = 3. Both functions are defined and continuous at x=2, so their values can be read from the graphs.

3. lim(f·g) = lim(f)·lim(g) = 0·(3/2) = 0. Both functions are defined and continuous at x=0, so their values can be read from the graphs. We doubt that g(0) = 3/2 exactly, but it doesn't matter since f(0) = 0.

4. lim(f/g) = lim(f)/lim(g) = 0/(3/2) = 0. See the explanation for 3, immediately above.

5. f(-1) = -2, which is the limit aproaching either from the left or right. √(3-2) = 1. The function f is defined and continuous at x=-1, so its value can be read from the graph.