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英语翻译The tangent line approximation L(x) is the best first-de

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英语翻译
The tangent line approximation L(x) is the best first-degree(linear) approximation to f(x) near x=a because f(x) and L(x) havethe same rate of change (derivative) at
a.For a better approximation than a linear one ,let's try a second-degree(quadratic) approximation P(x).In other words,we approximate acurve by a parabola instead
of by a straight line.To make surethat the approximation is a good one,we stipulate thefollowing:
(i) P(a)=f(a) (P and f should have the same value at a.)
(ii) P'(a)=f'(a) (P and f should have the same value at a)
(iii)P''(a)=f''(a) (p and f should change at the same rate at a)
英语翻译The tangent line approximation L(x) is the best first-de
信用证的近似切线(x)是最好的一级(线性)逼近附近f(x)x =因为f(x)和我(x)有相同的变化速度(导数信息)
.一个好的逼近比呈线性关系,让我们试一试二级(二次)逼近P(x).换句话说,我们acurve抛物线的近似代替
由直线.使近似确定是好的,我们规定企业:
(我)P(a)= f(一)(P和f值应该有相同.)
(二)P”(一)=福”(一个)(P和f应该有相同的价值在一)
(3)P”(a)= f”(一)(P和f应该在同一速率改变在
这个才是对的.
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