## Calculus assignment...

I am doing a Calculus assignment and I can't find the commands for certain things.

1.Given the function f(x) = ((x+1)^2) / (1+x^2)

i) The domain of continuity of f(x)

ii) The intervals of increase and decrease of f(x) by using test points.

2. Use the IVT to prove existence of a root to the equation x^3 +10x^2 -100x +50=0 in the interval [-20,10]. Use again the IVT to show that there is a 1st root in [-17,-15], a 2nd toot in [0,1] and a 3rd root in [ 5,6]. Find or approximate those roots with Maple. (the bolded is what I need help).

## How to plot function using the solution of ODE?...

I want to plot E with respect to t.

I typed the sys of this equation and try to plot it with DEplot but failed.

This is the code

DEplot([sys], [x(t), y(t), E(t)], t = -25 .. 25, [[x(0) = -.3, y(0) = .2]], scene = [E(t), t], stepsize = 0.5e-1, linecolor = red, arrows = none);

The error is Error, (in DEtools/DEplot/CheckDE) derivatives must be given explicitly.

## Convert an equation with ln...

Im working on a assignment on maple. I have an equation of motion that looks like this:  v(t):= -g*t-vs*ln(r*t-m)+vs*ln(-m)
Im supposed to use this equation and solve it for t an later integrate it. Since the constant inside the ln is negative I end up with a annoying imaginary part. Is there any way to covert this equation so that the ln disappear, so that I can get a result whitout a imaginary part?

## Inflection Points?...

How would I find inflection points? I believe it would the same as if I was finding critical points for f '.

Function is:(7-x)*sin(x^2-7)

So would it be:

a:=fsolve(f2,-2.4..2.4);
b:=fsolve(f2,-2.4..-0.06);
c:=fsolve(f2,-0.06..2.4);
d:=fsolve(f2,1.49..3);
e:=fsolve(f2,-3 ..-1.52);

Plz and thanks!

## math problem!! (Newton's method)...

 Consider the following function.f (x) = ( x3 − 442x2 + 65107x − 3196058) e1/x f:=x->(x^3-442*x^2+65107*x-3196058)*exp(1/x);
 Use Newton's method to find all 3 roots (correct to at least 6 decimal places) of f (x). (Note that you might have to increase the 'Digits' variable to 15, i.e., Digits:=15, in order to get the required accuracy.)

but, it is wrong. can anyone tell me where is the wrong part?

## plot a 2D arc in a coordicates which is in 3D coor...

In a local coordivates frame {B}, an arc whith center "coc" ,radius "radius" and angle between “alpha1” and “alpha2” can be plotted in XY plane of {B}. The coord {B} is in a Ref frame {O}. The homogeneous transformation matrix is “H”. How can I plot this arc in coordinate {O}？

## How to use Verlet algorithm to derive the orbit of...

Derive the orbit of the Moon around the Earth by doing a Verlet algorith of Molecular Dynamics simulation. Use one hour for your step τ. Place the stationary Earth at the origin of the Cartesian system. For initial conditions, use the position and the speed of the Moon when it is at its apogee (furthest from Earth). Plot the orbit.

## How to solve Cauchy sequences...

(a) Show that if {an} ∞ n=1 is Cauchy then {a 2 n} ∞ n=1 is also Cauchy. (b) Give an example of a Cauchy sequence {a 2 n} ∞ n=1 such that {an} ∞ n=1 is not Cauchy

## How to compute direct exponentiation of the matrix...

Hi EveryOne!

In the the answer of the question "How to find k^th root of the given matrix over finite field (at URL: http://www.mapleprimes.com/questions/203997-How-To-Find-Kth-Root-Of-The-Given-Matrix#comment215683). Carl Love helped to find k^th root of the given matrix M over GF(2m)/f(x).

Now, I need to compute direct exponentiation of the given matrix M in finite field. (If M = [mi,j], we say Direct Exponent (element-wise exponent matrix), Mdk of M is a matrix whose each element is the result of exponentiation of corresponding elements of M. If k=2, then we say Md2 is a direct square matrix of M )

## varying initial conditions...

Restrict calculation to real numbers.

Using y' = u, express the oscillator equation: y" + 3y' + 2y = cos(t) as a first order system.

Plot an approximate solution curve for the specified initial conditions.

[x0=5, y0=1],[x0=-2, y0=-4],[x0=0, y0=.1],

This is what i have so far but i am not sure if its correct.

Eulers modified method:

with(RealDomain);

x[0] := 0;

y[0] := 5;

t[0]=0

h := .1;

for n to 100 do

x[n] := x[n-1]+h*(x[n-1]+y[n-1]);

k1 := x[n-1]+y[n-1];

k2 := h*k1+x[n]+y[n-1];

k := 1/2*(k1+k2);

y[n] := h*k+y[n-1]

end do;

data := [seq([x[n], y[n]], n = 0 .. 100)];
G1 := plot(data, style = point, color = "blue");
G1;

## how do you find the horizontal asymptotes?...

1. Work with the function

f(x) = 5x^2-125/x^2-16

1. Find the horizontal asymptotes
2. Draw the graph of the function.  Show all horizontal and vertical asymptotes on your graph.  Edit the domain and the range to get a “good window” that clearly shows the shape of the function and all the important features, such as zeros, intercepts, maxima and minima, horizontal and vertical asymptotes.

## Maple Help ASAP...

I am new to maple and I need help.

Let x=x(t) and y=y(t) be functions in t. Suppose that x'=2x−5y+t and y'=4x+9y+sint such that x(0)=y(0)=0. Find y(1).

How do I go about doing this question?

Thanks

## How to find k-th root of the given matrix over fin...

Hi EveryOne!

In the the answer of the question "How to find roót of polynomial in finite field and extension finite field (at URL: http://www.mapleprimes.com/questions/203977-How-To-Find-Roots-Of-Polynomial-In-Finite#answer215097). Carl Love helped compute eigenvalues (x1,x2,...,xn)and eigenvectors of the given matrix M over GF(28)/(y^8+y^4+y^3+y+1).

I need to do:

1. Get matrix D from these eigenvalues (x1,x2,...,xn), with D[i,i] = xi and D[i,j≠i] = 0 (D will be diagonalizable matrix. Some xi may be in extension finite field  GF((28)2))

2. Get matrix P from eigenvectors corresponding to the above eigenvalues, compute P-1

3. Compute matrix B = P x D1/4 x P-1 in  extension finite field  GF((28)2).