## 30 Reputation

7 years, 326 days

## How to plot animation of taylor series?...

Maple

Knowing that the Taylor series for cos(x) is:
sum := sum+(-1)^i*x^(2*i)/(2*i)!

How would I write the following Maple code?

Generate an animation sequence showing the Taylor series approximation of cos(x) from N=1..10, where N is the number of terms in the series. Each subsequent frame of the animation should show a more accurate representation of cos(x) than the previous one. Plot the animation from x = -2*Pi .. 2*Pi, y = -5 .. 5

## Least Squares to Fit Curve...

Maple

From some scientific experiments, the following set of data is available
(1.0, 2.33),(2.0, 0.0626),(3.0, −2.16),(4.0, −2.45),(5.0, −0.357),(6.0, 2.21),(7.0, 2.75),(8.0, 0.636),(9.0, −2.45).

We need to use least squares method to fit the curve to the data
y = a + b cos(x) + c sin(x) + d cos(2x) + e sin(2x)

plot the data and the y curve together on the same graph to visualize the fitting. For the
data, use blue circles while for the y curve, use red solid line style. Use the leastsquares
command we learned in LinearAlgebra package.

## Solving system of Equations...

Maple

What is the solution to the following system? Is the solution unique? Use
the reduced row echelon form to explain why.
x + 2y + 3z = 1,
4x + 5y + 6z = 1,
7x + 8y + 9z = 1

## How to estimate the largest eigenvalues?...

Maple

Find the eigenvalues and eigenvectors for

A =
2 0.37 0
0 1.1 −4.29
1.6 0 2.2

Can you estimate the largest eigenvalues (in absolute value) using Power method for this
problem? Try to explain why if you can