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3 Written questions

3 Multiple choice questions

  1. Suppose two functions f(x) and g(x) are differentiable around a and g'(x) does not equal zero, Then iff trying to find the limit as x approaches a of f(x)/g(x) and the limit of f(x) and g(x) both equal zero, or both equal infinity, then the limits of indeterminate form can be evaluated by taking the derivative of both f(x) and g(x).
  2. 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
  3. How fast f(x) is increasing or decreasing at the point x = a

2 True/False questions

  1. Average Rate of Change[f(b) - f(a)] / (b-a)


  2. 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)