How do we find our approximation for #2.9^5#?
2 Answers
Sep 24, 2016
See explanation
Explanation:
2.9=29/10 is a rational number of the form integer/integer..
And so,29#/1010)^5 = 20511149/100000 is rational.
The exact value in decimals is 205,11149.
Successive rounded approximations are
3-significant digits ( sd:): 205
4-sd: 205.1
5-sd: 205.11
6-sd: 205.111
6-sd: 205.1115.
You can try instead the binomial expansion for
Sep 24, 2016
We can also use the approximation of
The derivative of
The point it intersects is
Thus the tangent line is
Thus, an approximation for
#y=405(2.9)-972=202.5# .
This compares to the actual value of