Taylor series and quadratic approximation

ookt2c
Messages
16
Reaction score
0

Homework Statement



use an appropriate local quadratic approximation to approximate the square root of 36.03

Homework Equations



not sure

The Attempt at a Solution



missed a day of class
 
Physics news on Phys.org
ookt2c said:

Homework Statement



use an appropriate local quadratic approximation to approximate the square root of 36.03

Homework Equations



not sure

The Attempt at a Solution



missed a day of class

You need to rwwrite
\sqrt{36+0.03}
in the form 6 \sqrt{1+\epsilon} and then expand this to order epsilon squared. I will let you figure out what the value of epsilon is.
 

Thread 'Prove that the integral is equal to ##\pi^2/8##'

Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
View full post »

Similar threads

How should I show that this root is given approximately by this?
Replies
2
Views
2K
Link between Z-transform and Taylor series expansion
Replies
2
Views
2K
Taylor polynomial, approximative solution of this equation
Replies
3
Views
1K
Evaluate the Taylor series and find the error at a given point
Replies
6
Views
3K
Using a Taylor expansion to prove equality
Replies
1
Views
1K
Taylor Series Error Integration
Replies
6
Views
4K
How Does Including the Quadratic Term Affect the Newton Iteration Formula?
Replies
1
Views
2K
[Calc II] quadratic Chebyshev approximation
Replies
2
Views
2K
Find the limit using taylor series
Replies
11
Views
3K
What is the Taylor expansion of x/sin(ax)?
Replies
5
Views
3K

Hot Threads

Recent Insights

Back
Top