APPENDIX 3

Auxiliary Material

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A3.1 Formulas for Special Functions

For tables of numeric values, see Appendix 5.

Exponential function ex (Fig. 545)

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Natural logarithm (Fig. 546)

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ln x is the inverse of ex, and elnx = x, e−ln x = eln (1/x) = 1/x.

Logarithm of base ten log10x or simply log x

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log x is the inverse of 10x, and 10logx = x, 10−log x = 1/x.

Sine and cosine functions (Figs. 547, 548). In calculus, angles are measured in radians, so that sin x and cos x have period 2π.

sin x is odd, sin (−x) = −sin x, and cos x is even, cos (−x) = cos x.

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Fig. 545. Exponential function ex

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Fig. 546. Natural logarithm ln x

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Fig. 547. sin x

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Fig. 548. cos x

Fig. 549. tan x

Fig. 550. cot x

Tangent, cotangent, ...

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