Chapter 2.3, Problem 61E

limi Use the three conditions to determine whether f(x) = is continuous at x = x--169 13. If it is discontinuous, identify the type of discontinuity. If the discontinuity is removable, remove the discontinuity by redefining the function.

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Va +t - Va -t lim t 0 for a > 0

3. How is the continuity of the following function at x=0? • There exist Left continuity ● Right continuity • Does not exist X X x=0 2 x = 0 f(x) = X (1)

riemann fuction

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Definition: Let f: A → R be a function defined on a set A containing the point c. We say that f is differentiable at c (or has a derivative f'(c) at c) if the limit below exist and is finite ƒ'(c) = lim X→C f(x) − ƒ(c) X-C We say that f is differentiable S ≤ A iff f'(c) exists for all c E S. The function f':S → R is called the derivative off on S. 1 a) f(x) =,x>0 b) f(x)=√x,x ≥0 Use the definition above to find the derivative of each function and determine the subset of its domain at which the derivative f' exists.

Question: Explain a method that could be used to find the absolute maximum and minimum values of a continuous function fon a closed interval [a, b]. Apply this to a continuous function on a closed interval.

How do I evaluate the limit of this function? I am currently in Calculus one and going through the Mean Value Theorem.