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高数题,关于Taylor多项式的

学习 时间:2026-04-08 23:32:18 阅读：6292
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?
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明理的网络

怕黑的日记本

2026-04-08 23:32:18

(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! * x³for 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

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  • 害怕的猎豹
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    2026-04-08 23:32:18

    (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! * x³for 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

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