## Analytic Functions and matrices...

I am trying to find a easy way to use analytic functions with matrices. For example A:= 2x2 matrix (that is diagonalizable) then cos (A) = P L P^1 where P is the matrix made of the eigen vectors and L is the matrix of eigen values along the main diagonal. While I can work these problems by figuring the parts (P L P^1) I would prefer to find a way to be able to just write cos(A). I figure there is a syntax that I am failing to use properly to use this function with a matrix input. Any help would be appreciated.

## maximum and minimum points...

hey i have the equation y=3X^4+2X^3-15X^2+13X+3 I need to find the (x,y) values of the maximum and minimum points to 3sf. im not too good with computers can anyone help me

## matrix computation...

Dear Sir: I am still a novice to use the maple. Please give some advice for the following code. Expecially, I try to construct the final P(3x3) matrix. In the for-loop, normalized vectors are generated. Then, those are converted into a matrix. But, I do not know how to write a code. restart: with(LinearAlgebra): interface(displayprecision=4): mass:=Matrix([[m[1],0,0],[0,m[2],0],[0,0,m[3]]]); stif:=Matrix([[k[1]+k[2],-k[1],0],[-k[1],k[1]+k[2],-k[2]],[0,-k[2],k[2]]]); m[1],m[2],m[3],k[1],k[2],k[3]:=4,4,4,4,4,4; msri:=simplify(MatrixFunction(mass,sqrt(x),x)^(-1)); mass2:=msri.mass.msri; stif2:=msri.stif.msri;

## simple alg; x=3/2 y-1/2...

x=3/2 y-1/2 Three over two times y minus one over two for the previous question.

## Simple algebra problem...

This is surely the equivalent of using an elephant gun to go after an ant but in any case. Could someone tell me how to sub in four values for y, -2,0,1.5 and 3, one at a time in this equation: 3 1 x = - y - - 2 2 I am only using document mode but can not figure out how to automate this type of problem. I am able to manually sub in the value but I am too lazy to do all that work. Also is there any way to show the steps of the solution and not just pop out the answer?

## Draw Temp Graph for certain Timeframe...

How do I graph the first 30 minutes of this problem? T = 32+127*exp(-.3456*30) Also, when this is graphed, it is supposed to show a horizontal asymptote.

## Nested Loops...

I am trying to populate a matrix using a nested for..from loop. The Maple statments below only populate the first column; any suggestions? > for i to 45 do for j from 0 by 5 to 45 > do A[i, j+1] := evalf(EllipticF(sin(i*deg2rad), sin(j))); > end do; > end do; Thank you for the assistance.

## peicewise functions...

Hello, I am given a question in the form f(x)=x^delta sin(1/x) if x does not equal zero,and f(x)=0 if x = 0. the question goes on to say, where delta > 0, we know that f is continous at x=0, but is differentiable at x=o only when delta > 1. it asks me to use maple to provide evidence for this using MAPLE,s graphing features. I am not sure how to input this into MAPLE. Could someone please help? thank's a bunch I think i posted this in the wrong section before.

## piecewise functions...

Hello, I am given a question in the form f(x)=x^delta sin(1/x) if x does not equal zero,and f(x)=0 if x = 0. the question goes on to say, where delta > 0, we know that f is continous at x=0, but is differentiable at x=o only when delta > 1. it asks me to use maple to provide evidence for this using MAPLE,s graphing features. I am not sure how to input this into MAPLE. Could someone please help? thank's a bunch

## derivitives...

how do i determine the derivitive of y=lnsinx-(1/2sin^2x)

## How to draw a scatterplot?...

I need to plot about 44 points on an X-Y graph. All the X coordinates are given (imported from Excel) as a list. All the Y coordinates are given as a separate list. For example (roughly this is what the order of magnitudes are of the X and Y variables) X:=[380,4000,4067,...,5789] Y:=[10, 35, 56,...,82] So plot (380,10) (4000,35) (4067, 56)... (5789,82) I will worry about curve fitting and all that stuff later. I would first and foremost like to see Maple understand my data and plot it.

dear Maple Masters, i have a plotting problem about the equation |x|+|y|=5. the plot shows strange corners of the rectangle, which is absolutely incorrect as far as i'm concerned. am i wrong? or is this a bug?