微積分兩題求詳解

👨🏻‍🏫 學術台數學

[匿名]

2009-10-26 6:06 pm

1. Consider h(x) = ln x
A. Find the linear approximation for h(x) at the point where a=1
B. Use the approximation found in part A

2. Consider F(x) = tan x
A. Find the linear approximation to f(x) at the point ( 拍/4, 1)
B. Use the approximation found in part A to estimate tan 3拍/10. Answer in terms of 拍.

更新1:

第一題我想通了求第二題!!! 拜託高手

更新2:

sqrt是什麼!!

更新3:

我知道了!!!! 真的很感謝!!!

回答 (1)

Prof. Physics

2009-10-26 9:40 pm

✔ 最佳答案

2. F(x) = tanx

F'(x) = sec^2x

Using linear approximation,

F(x) = F(pi/4) + F'(pi/4)(x - pi/4)

F(x) = tan(pi/4) + sec^2(pi/4)(x - pi/4)

F(x) = 1 + (x - pi/4)sqrt2

F(x) = (1 - pi(sqrt2)/4) + x(sqrt2)

b. Put x = 3pi/10

tan(3pi/10)

= (1 - pi(sqrt2)/4) + (3pi/10)(sqrt2)

= 1 + pi(sqrt2)/20

參考: Physics king

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