Suppose you are asked to find the Linear Approximation of 𝑓 ( 𝑥 ) = tan 𝑥 at 𝑥 = 𝜋 4 . Remember that the Linear Approximation is given by: 𝐿 ( 𝑥 ) = 𝑓 ( 𝑎 ) + 𝑓 ′ ( 𝑎 ) ( 𝑥 − 𝑎 ) (a) What is 𝑓 ( 𝜋 4 ) ? [ Select ] 2/sqrt(3) 1 -1 0 1/sqrt(2) (b) What is 𝑓 ′ ( 𝑥 ) ? [ Select ] f'(x)= sec^2x f'(x)= tan x f'(x) = sec x tan x f'(x) = sec x f'(x) = tan^2 x (c) What is 𝑓 ′ ( 𝜋 4 ) ? [ Select ] 1 2 sqrt(2) 0 4 1/sqrt(2) 多重下拉选择题
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at 的线性近似值为： 提示：at 的线性近似值为： 。
The linear approximation of 𝑓 ( 𝑥 ) = 5 𝑥 − 4 2 𝑥 2 + 1 at 𝑥 = − 3 is: Hint: The linear approximation of 𝑦 = 𝑓 ( 𝑥 ) at 𝑥 = 𝑥 0 is: 𝐿 ( 𝑥 ) = 𝑓 ′ ( 𝑥 0 ) ( 𝑥 − 𝑥 0 ) + 𝑓 ( 𝑥 0 ) .
This is a continuation of the previous question. What is the Linear Approximation of 𝑓 ( 𝑥 ) = tan 𝑥 at 𝑥 = 𝜋 4 ?
Suppose you want to use a Linear Approximation to approximate 1 25.2 without a calculator. Which of the following functions and 𝑥 -values would be best to use?
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