How do you use linear Approximation to find the value of #(1.01)^10#?
2 Answers
with two significant digits.
Explanation:
Consider the function:
We have:
Develop in MacLaurin series and stop at the linear term:
Then we have for
Consider now the second derivative:
For
or:
So, using Lagrange's formula:
we have:
Using a calculator you should get
Explanation:
Here's a slightly simpler, less comprehensive answer.
We let
Now use the linear approximation formula, which is
Our point will obviously be
Also,
Plugging this into our formula, we have:
#y = 1+ 10(0.01) = 1.1#
Note that this is a rough approximation. The further away you get from the point
Hopefully this helps!