一.程序：Series[ArcTan[x], {x, 0, 20}]
结果：SeriesData[x, 0, {1, 0,
Rational[-1, 3], 0,
Rational[1, 5], 0,
Rational[-1, 7], 0,
Rational[1, 9], 0,
Rational[-1, 11], 0,
Rational[1, 13], 0,
Rational[-1, 15], 0,
Rational[1, 17], 0,
Rational[-1, 19]}, 1, 21, 1]
---------------------------------------------------------------------------------------------------------
第二问描述图形没看懂
-------------------------------------------------------------------------------
模型：DSolve[{x'[t] == a x[t]}, x[t], t]
{{x[t] -> E^(a t) C[1]}},代入边界条件 x[t0]=x0,所以 x[t]=x0*exp[a t]
(1)x[t_] := Subscript[x, 0] Exp[a t];
Subscript[x, 0] = 1.25909*10^9;
a = 14.8*10^-3;
t = 2010 - 1999;
x[t]
j结果1.4817*10^9
（2）Clear[a]
NSolve[x[50] == 1.4*10^9, a]；
{{a -> 0.00212166}} 一.程序：Series[ArcTan[x], {x, 0, 20}]
结果：SeriesData[x, 0, {1, 0,
Rational[-1, 3], 0,
Rational[1, 5], 0,
Rational[-1, 7], 0,
Rational[1, 9], 0,
Rational[-1, 11], 0,
Rational[1, 13], 0,
Rational[-1, 15], 0,
Rational[1, 17], 0,
Rational[-1, 19]}, 1, 21, 1]
---------------------------------------------------------------------------------------------------------
第二问描述图形没看懂
-------------------------------------------------------------------------------
模型：DSolve[{x'[t] == a x[t]}, x[t], t]
{{x[t] -> E^(a t) C[1]}},代入边界条件 x[t0]=x0,所以 x[t]=x0*exp[a t]
(1)x[t_] := Subscript[x, 0] Exp[a t];
Subscript[x, 0] = 1.25909*10^9;
a = 14.8*10^-3;
t = 2010 - 1999;
x[t]
j结果1.4817*10^9
（2）Clear[a]
NSolve[x[50] == 1.4*10^9, a]；
{{a -> 0.00212166}}