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303. The value for x in the last example was obtained from a calculator and is rounded off. Exercise 22. 1). CHAPTER 1. 16) by loga (b). 15. 17) or expa (loga (b)) = b. Here are some sample logarithms for the base 2: log2 4 = 2 log 2 (1/8) = −3 log2 16 = 4 log2 √ 2 = 1/2 and for the base 10: log10 1 = 0 log10 100 = 2 log10 (1/10) = −1. Your calculator will give you good approximations for at least log10 (x) for any x > 0. Exercise 23. Find logarithms for the base 10: (1) log10 5 (3) log10 π (5) log10 25 (2) log10 100 (4) log10 (1/4) (6) log10 1.

10: The function f (x) and one secant line. 11: The slopes of secant lines, the function g(x). Exercise 42. Find the average slope of the function sin x over the interval [π/6, π/3].

We demonstrate this idea first with two examples. In the first example we use the exponential function to illustrate several ideas which enter into the general definition of the derivative. In the second example we take a geometric approach and interpret the tangent line in a special case. The geometry tells us what the derivative of the function is, or should be. 2 on page 43. The requirement that the difference between the graph and the tangent line is small is expressed analytically in terms of an inequality.

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Applied calculus by Dovermann K.H.

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