Question

Use linear approximation, i.e. the tangent line, to approximate 1/0.104 as follows: Let f(x)=1/x and find the equation of the tangent line to f(x) at a "nice" point near 0.104 . Then use this to approximate 1/0.104 .

L(x)=f(a)+f'(a)(x-a)...i think.


You're notation is slightly different than I use, but yes, that is how to make a linear approximaton.
You're using
L(x)=f(a)+f'(a)(x-a)
whereas I use
f(x+dx)=f(x)+f'(x)dx which is the differential notation I was taught.

If f(x)=1/x = x^-1 , then caluclate f'(x) = -x^-2.
The "nice" point near 0.104 'might' be .1 since 1/.1 = 10. Now calculate f'(.1) = -.1^-2 = -100
Then dx =.004
Then using
L(x)=f(a)+f'(a)(x-a)
L(.104)=f(.1) + f'(.1)*.004
L(.104) =approx. 10 + -100*.004

The correct answer is 9.61538... so you can see the approximation is good to one decimal place.

Answer 1

Where did the .004 come from ?