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近似计算

近似计算. 简单近似计算公式 [当| x |<<1 时]： f ( x )  f (0)+ f  (0) x (1  x ) n  1  n x (1 + x )  1/ n  1 ( x / n ). sin x  x cos x 1( x 2 /2) 1 tan x  x ln(1+ x )  x e x 1+ x+ ( x 2 /2) 1+ x.

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近似计算

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  1. 近似计算

  2. 简单近似计算公式 [当|x|<<1时]： f(x)f(0)+f(0)x(1x)n1nx(1+x)1/n1(x/n)

  3. sinxx cosx1(x2/2)1tanxxln(1+x)x ex1+x+(x2/2)1+x

  4. [例1] 估算301/3的数值.301/3={27[1+(1/9)]}1/33[1+(1/3)(1/9)] =3+(1/9)3.111 [实际301/33.107]

  5. [例2] 估算e0.237的数值.e0.2371+0.237 +(0.2372/2)1.265 [实际e0.237 1.267]

  6. 为了估算指数函数或对数函数的数值，请记住以下5个数的对数值：lg2=0.30103 lge=0.43429 lg3=0.47712 lg7=0.84510 ln10=2.3026

  7. [例3] 估算ln20.086的数 值.ln20.086=ln20+ln1.0043 =ln10lg20+ln(1+0.0043)2.30261.3010+0.0043 3.0000 [实际ln20.086 3.0000]

  8. [例4] 估算ln760的数值.ln760=ln800+ln0.950 =ln10lg800+ln(10.050)2.30262.90310.050 6.635 [实际ln760 6.633]

  9. [例5] 估算2100的数值. 2100=10100lg2 101000.30103 =1030100.103 =1030e0.103ln10 1030e0.1032.301030e0.237 1.2651030 [实际21001.2681030]

  10. 实际上，人们知道的每件事都只是某种近似，…… ——理查德·费曼

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