NAME

### Question limit

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### 3 Multiple choice questions

1. If f(x) is continuous on the closed interval [a, b], differentiable on (a, b), and satisfies f(a) = f(b), then for some c in the interval (a, b), we have f'(c) = 0
2. If the limit as h approaches zero of [f(a+h) - f(a)] / h exists, then the limit is differentiable at x=a. Notation: f'(a)
3. If f(x) is continuous in an interval [a, b] then somewhere on the interval it will achieve every value between f(a) and f(b); if f(a) is less than or equal to M, which is less than or equal to f(b), then there exists one value c in the interval [a, b] such that f(c) = M.

### 2 True/False questions

1. Definition of ContinuityIf the limit as h approaches zero of [f(a+h) - f(a)] / h exists, then the limit is differentiable at x=a. Notation: f'(a)

2. Instantaneous Rate of Change[f(b) - f(a)] / (b-a)