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Find, to 10 significant figures, the unique turning point x0 of f(x)=3sin(x^4/4)-sin(x^4/2)in the interval [1,2] and enter it in the box below.x0=？

How to write this in maple？

Hello, 

I am trying to solve a simple equation 

x(0.0178){tan([2.10^-5](x)^0.5)}^2=+2.32.10^12-x, which I want to be solved over the range 1.10^10......2.10^12.

I have tried the following program (which I have got help on):

restart; 

eq := x(0.0178)*tan²(Sqrt(x)*2E-5) = 2.32e12-x;

Use Newton’s Method to approximate the indicated root of the equation to correct six decimal places.

The root of 2.2x⁵ – 4.4x³ + 1.3x²-0.9x-4.0=0 in the interval [-2, -1].

The rest of the assignment states : "

Start by plotting the function in
Maple to get a reasonably good initial approximation. You may use a
“while” loop, but do not use existing Maple commands for Newton’s

The question is to use a program of modified newton raphson , incorporating the Romberg intergal procedure which i have already created, to create a new program which evaluates the integral f(alpha) = 1-10*int(tan(x)^alpha),from 0 to Pi/4.
The following needs to be incorporated in your program:

-Let ci be the approximation of alpha* on iterate i of your "modified newton raphson" method, then the program should run until:
             |ci-c(i-1)|<10^(-6)

Dear Primers

I have an exponantial equation of the form below:

eq161 := 1/2*alpha^4*(-2*exp(-1+1/2*(4*alpha^2+1)^(1/2)+1/2*(-4*alpha^2+1)^(1/2))*(4*alpha^2+1)^(1/2)+2*exp(-1+1/2*(4*alpha^2+1)^(1/2)-1/2*(-4*alpha^2+1)^(1/2))*(4*alpha^2+1)^(1/2)-2*exp(-1+1/2*(4*alpha^2+1)^(1/2)-1/2*(-4*alpha^2+1)^(1/2))*(-4*alpha^2+1)^(1/2)+2*exp(-1-1/2*(-4*alpha^2+1)^(1/2)-1/2*(4*alpha^2+1)^(1/2))*(-4*alpha^2+1)^(1/2)+2*exp(-1+1/2*(-4*alpha^2+1)^(1/2)-1/2*(4*alpha^2+1)^(1/2)...

I came across this problem while helping another user find the maxima of an expression for 
various values of a parameter here:

http://www.mapleprimes.com/questions/124104-Maximum-Points--Of-Function-With-More

For various values of ga, it was required to find the maxima in a range of 0<delta<2. 
Plots of the expression indicate that one such maxima exists for each value of the parameter.

My approach was to find the zeros of the first...

I want to find the first positive and first negative root of a bessel function

j2 := (x, a) -> k(x)^2*a^2*(diff((diff(1000000000*sin(1/1000000000*k(x)*a)/(k(x)*a), x))/(k(x)*a), x))/(k(x)*a)

I couldn't use the built in bessel function with two variables, so I had to enter it by hand.

I want to find the values of x where j2 is zero as a function of a:

f := (a) -> RootOf(j2(x, a), x, 0 .. 2)

plot(f(a), a = 2 .. 2.25, y = -3 .. 3)

I am trying to solve this set of equations ,but i have spent a lot of time rewriting the equations and changing the signs..but i cant get rid of this erroe and solve it for the unknowns.....could anyone tell me what am i doing wrong ?

There have been a few posts on mapleprimes about numerically solving systems of procedures. The latest one, up until now, was this.

Here's some code to implement the method. Since the algorithm is basically very simple, I've added a few bells and whistles as optional arguments.

The essence of it is as follows. The number of procedures must match the number of parameters of each and every procedure. It does maxtries attempts at choosing a random point, and then does at most maxiter iterations. A solution is only accepted if the norm of the last change in vector (point) x is less than xtol, and if the forward error norm(F(x)) is less than ftol. The jacobian of F may be supplied optionally as a Matrix of procedures, or a method for computing the jacobian may be supplied. The methods are fdiff which only uses Maple's numerical differentiation routine fdiff, or hybrid which attempts symbolic differentiation via Maple's D[] operator and then falls back to fdiff via the nifty evalf@D equivalence.

In a comment to a Mapleprimes thread, Jacques mentioned an old suggestion of Kahan's that numerical computations should return an estimate of conditioning alongside a result.

I mentioned in this comment an approach for numerical estimation of (all) roots of a univariate polynomial with real or complex numeric coeffficients that is based upon computing eigenvalues of a companion matrix. Here below is some rough code to inplement that idea, but which also returns condition number estimates associated with the eigenvalues.

I include an example of the badly conditioned Wilkinson's polynomial. It is possible that better results could be obtained by using a Lagrange basis representation of that polynomial, but I didn't try to figure out how that would work in an analogous way. The standard Maple utility, fsolve, has no problem with this example.