Use the linear approximation formula to approximate tan 1 ta

Use the linear approximation formula to approximate tan .1. tan. 1 ~ 0.1003347 tan. 1 ~ 0.1 tan. 1 ~ 0 tan. 1 ~ -0.1

Solution

Solution:

linear approximation
f(x) = f(a) + f\'(a) dx

tan(0.1)
a = 0
dx = 0.1
f(x) = tan x

f\'(x) = Sec^2 (x)
f\'(a) = Sec^2 (a)

f\'(0) = Sec^2 (0)

f(0.1) = tan 0 + sec^2 (0) *(0.1) = 0.1

So tan 0.1 = 0.1