Question

Fill in the blank with “all,” “no,” or “some” to make the following statements true. • If your answer is “all,” explain why. • If your answer is “no,” give an example and explain. • If your answer is “some,” give two examples, one for which the statement is true and the other for which the statement is false. Explain your examples.

1. For functions g, if lim x→a+ g(x) = 2 and lim x→a− g(x) = −2, then limx→a (g(x))2 exists.

2. For functions f and g, if limx→a f(x) exists and limx→a (f(x) + g(x)) exists, then limx→a g(x) exists.

3. For real numbers x, the functions f(x) = (x^2 − 9)/(x − 3) and g(x) = x + 3 are equal.

4. For real numbers a, limx→a f(x) = f(a).

Answer 1