52 791
Assignments Done
98,1%
Successfully Done
In October 2017
Your physics homework can be a real challenge, and the due date can be really close — feel free to use our assistance and get the desired result.
Be sure that math assignments completed by our experts will be error-free and done according to your instructions specified in the submitted order form.
Our experts will gladly share their knowledge and help you with programming homework. Keep up with the world’s newest programming trends.

Answer on Calculus Question for Imee Carla

Question #1751
How can I use the concept in differentials to approximate a certain number which is not a perfect square?
Expert's answer
You can expand the function of square root in a series :
We can represent the number as a sum of nearest perfect square root R and the difference of the number and this sq.root (N-R), it can be both positive and negative.
f(x) = √N = √(R + (N-R)) = √R √(1 + (N-R)/R).

Denote (N-R)/R as α , |α|<1. The function √(1 +α) can be represented as a sum:
√(1 +α)= 1 + 1/2 α - 1/8 α2 + 1/16 α3 - 5/128 α4 + ... This expression was obtained by expanding the function √(1 +α) in a Teylor series in neiborhood of 1. √(1 +α) = sum from n=0 to infinity ( f(n)(1)/n! αn ), where f(n) (1) the n-th derivative of the function f(a)=√x at the point x = 1.
Thus the final fomula would be as
√N = √R (1 + 1/2 α - 1/8 α2 + 1/16 α3 - 5/128 α4 +...), where α = (N-R)/R

Need a fast expert's response?

Submit order

and get a quick answer at the best price

for any assignment or question with DETAILED EXPLANATIONS!

Comments

No comments. Be first!

Leave a comment

Ask Your question