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3 Written questions

3 Multiple choice questions

  1. 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. 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).
  3. [f(b) - f(a)] / (b-a)

2 True/False questions

  1. Definition of ContinuityIf the limit of f(x) as x approaches a exists, and the limits are equal to f(a) at the point and from both sides, then f(x) is continuous at x=a


  2. Instantaneous Rate of ChangeHow fast f(x) is increasing or decreasing at the point x = a


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