Chapter 10: Q. 1 (page 782)
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Find .
Consider the function f shown in the graph next at the right. Use the graph to make a rough estimate of the average value of f on [−4, 4], and illustrate this average value as a height on the graph.
Suppose that we know the reciprocal rule for limits: If exists and is nonzero, then This limit rule is tedious to prove and we do not include it here. Use the reciprocal rule and the product rule for limits to prove the quotient rule for limits.
Use the definition of the derivative to find for each function in Exercises 39-54
Consider the sequence of sums
(a) What happens to the terms of this sequence of sums as k gets larger and larger?
(b) Find a sufficiently large value of k which will guarantee that every term past the kth term of this sequence of sums is in the interval (0.49999, 0.5).
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