灵鹊做题网高数题,关于Taylor多项式的
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高数题,关于Taylor多项式的
题目请看图片
a b 只要套用公式就行了把 c前半部分是估计数值,这个没多大问题,但后面那个upper and lower bound是什么,该怎么求?
题目请看图片
a b 只要套用公式就行了把 c前半部分是估计数值,这个没多大问题,但后面那个upper and lower bound是什么,该怎么求?
(a)
P2(x) = x - x²/2
(b)
When x=0, Taylor's Formula is called Maclaurin Formula, Using the Lagrange error bound:
R2(x) = f(3)(c)/3! * x³
for f(x)= log(1+x）
R2(x) = x³/3(1+c)³ where c is between 0 and x ；
(c)
as for log(1.5)=log(1+0.5), let x=0.5, thus:
P2(0.5) = 0.5 - (0.5)²/2 = 0.375
[where log(1.5)=0.405465108108164381978013115464...]
R2(0.5) = (0.5)³/3(1+c)³ where 0
P2(x) = x - x²/2
(b)
When x=0, Taylor's Formula is called Maclaurin Formula, Using the Lagrange error bound:
R2(x) = f(3)(c)/3! * x³
for f(x)= log(1+x）
R2(x) = x³/3(1+c)³ where c is between 0 and x ；
(c)
as for log(1.5)=log(1+0.5), let x=0.5, thus:
P2(0.5) = 0.5 - (0.5)²/2 = 0.375
[where log(1.5)=0.405465108108164381978013115464...]
R2(0.5) = (0.5)³/3(1+c)³ where 0