Errors in approximations Carry out the procedure described in Exercise 77 with the following functions and approximations.
f(x) = tan x, p1(x)= x,
Solution 81E
Step 1:
Given , f(x) = tan(x) , , and
By , using Exercise 77 with the given functions and approximations are ;
tan (0.2) = 0.2027100355 , ,
And =  0.2 0.00266667 = 0.200266667
tan(0.1) = 0.100334672 , ,
And =  0.1 3.3333333 = 0.1003333333
tan(0) = 0 , , And = 0
tan(0.1) = 0.100334672 , ,
And = 0.1 + 3.3333333 = 0.1003333333
tan (0.2) = 0.2027100355 , ,
And = 0.2 +0.00266667 = 0.200266667
x 
Error = tan(x)   
Error = tan(x)   
0.2 
Error = 0.2027100355 +0.2
= 0.0027100355 
Error = 0.202710035+0.200266667
= 0.002443368

0.1 
Error = 0.100334672 +0.1
= 0.000334672 
Error = 0.100334672+0.1003333333
= 0.00000134

0 
Error = 00 =0 
Error = 00 = 0 
0.1 
Error =  0.100334672  0.1
= 0.000334672 
Error = 0.100334672 0.10033333
= 0.000001342 
0.2 
Error =  0.20271003550.2
= 0.0027100355 
Error = 0.2027100355  0.200266667
= 0.0024433685 