## Error in calculus sheet...

Hello Maple

I am preparing for an examination in Calculus, but my worksheet in Maple 18 doesn't cooperate.

A lot of my studypartners use Maple 16 and they have no problems.

I meet the following error:

- Error, (in solve) invalid input: hastype expects 2 arguments, but received 1

I'm totally sure, that I'm typing correctly, because I write just the same as my studypartners.
So is it an error, which only is seen in Maple 18 and can I do anything to solve the problem?

Kind regards
Anders Kristensen

PS: I can't figure out how to add a picture

## how do you do a vertical disk method?...

I have to find the volume of a solid using the disk/washer method and the shell method.  I think I have the first part(disk/washer) right.   I think the shell is off. The problem is "the region in the first quadrant that is bounded above by the curve y = 1/x^1/4, on the left by the line x = 1/16, and below bythe line y = 1 is revolved about the x-axis to generate a solid."    I am having computer problems so any help is appreciated. Thanks

## update to Clickable Calculus Study Guide

by: Maple

For those who have the Clickable Calculus Study Guide for Maple 18, please note that we have released an update to this ebook, which provides corrections and improvements to the text and examples.

eithne

## using maple to find the dimensions of a right cyli...

I under stand how to do the calculus that's easy enough, but Maple is stil giving me a hard time.  The math par t is let the radius of the cylinder be r cms. 0<r<10 Then the height is 2 * Sqrt 100-r^2, the volume is V(r)=2PIr^2* sqrt 100-r^2 cm^3

Differentiante V(r) with respect to r we get V' (r) =2PIr^2(1/(2*sqrt(100-r^2)))(-2r) + (2PIsqrt(100-r^2))(2r)

V'(r)=(-2PIr^3 +4PIr(100-r^2))/sqrt (100-r^2)      V'(r)=2PIr(200-3r^2)/sqrt 100r^2         to find the critical point find the value of r when V(r) =0     2PI(200-3r^2)/sqrt 100-r^2 =0   2PIr(200-3r^2) = 0   r(200-3r^2)=0

r=0 or 200-3r^2 =0     r=0 or r^2=200/3 r=sqrt(200/3) =10sqrt(2/3)   r is not in the interval so ignore it.  The critical point for 0<r<10 occurs at r = 10sqrt(2/3)       Since V'(r) >0 for 0<r<10sqroot(2/3) and V'(r) <0<10sqrt(2/3)<10

The dimensions are r=10sqrt(2/3) =8.16 cm and h=20/sqrt3 = 11.55 cm the volume is 4000PI/3*sqrt3=2418.4 cm^3

So how do I translate this into maple? Any help is greatly appreciated.

## apply convert(,exp) to matrix...

Hi all,

I am stuck with the following problem:

convert(cos(alpha), exp); works fine for me.

Once I have the trigonometric functions in a matrix, it does not work any more:

In the latter line, A keeps the trigonometric functions. Why is this the case? Is there any way to force maple to keep the complex exponentials instead of trigonometric functions?

I am using LinearAlgebra and VectorCalculus.

Best Regards

Wassja

## Multivariate Taylor expansion...

How can I expand the mutivariate taylor series of the functions below about the point (x,y)

f(h*a[2]+x, h*a[2]*k[1]+y);

and

f(h*a[3]+x, y+h(a[3]-b[32])*k[1]+h*b[32]*k[2]);

## Maple 17 Won't plot this ...

I copied and pasted this from the example page and I have to get this same graph for an assignment

im using maple 17

when i hit enter the return was

(1)

## Max/Min Problems in Maple 17...

Hello All,

I have had a few questions that have come up while working on a Maple Assignment for my Calculus III class. I was wondering if anybody could help me with these questions, as well as show me how to enter them in Maple. Here are the questions I have been struggling with.

1. In the xy-plane, graph the ellipse ((x-4)^2)/(4))+(y-4)^2=1 and two level curves of F(x,y)=x^3+y^3-3xy that just touch the ellipse.

a. What do we know about the gradients of F and the ellipse at those points?

b. Use your graph to approximate the minimum and maximum values of F subject to the constraint ((x-4)^2)/(4))+  (y-4)^2=1.

2. A company manufactures a product using inputs x,y,z according to the production function Q(x,y,z)=20x^(1/2)y^(1/4)z^(2/5). The prices per unit are \$7 for x, \$12 for y, and \$18 for z.

a. Create the cost function

b. The company wants to produce 2500 products. Estimate the minimum cost by using the graph of the level surfaces of the cost function (from part a) together with the production constraint.

## How to get CriticalPoints to return only valid cri...

I'm trying to use the CriticalPoints command from the Student[Calculus1] package to determine the critical points of f(x) = x^2 * ln(x).

 (1)

My issue is this. A critical point is defined as a value of x in the domain of f(x) where either f'(x)=0 or f'(x) does not exist. Clearly x=0 is not in the domain of f(x) = x^2*ln(x). How may I "trick" Maple into returning only the value exp(-1/2)?  As seen above, my attempt to use the assuming command proved futile.

More troubling, however, is whether or not the CriticalPoints command is using the correct definition to compute critical points. Can anyone shed some light on this?

## Sequence of real numbers...

A sequence of real numbers $a_1,a_2,a_3.......$ satisfies $a_0=1$ and

## Get area under curve from spreadsheet data...

If I have spreadsheet data, x and y (velocity and time), I need to find distance.  I see numbers of ways to do this, however, I wonder what people would suggest as the fastest / easiest way.  I'm not needing a function really, just results.  Does Maple have tools to simplyify this process, and if not, what process(s) might yield results of determinable or selectable accuracy.  I will have many sets of data in the future that need to be manipulated...

## using region fill in approximate integration...

The Single Variable Calculus Approximate Integration Tutor (and the function ApproximateInt) work fine for the built-in example of sin(x) from 0 to Pi.  But if you change it to sin(Pi*x) from 0 to 1 then plot options are ignored.  And if you ask to integrate sin(3.1415926*x) from 0 to 1, then it works again.  Is there a work-around?

## Calculus Study guide disappointment...

I got Maple 17 a few weeks ago and it has been helpful in my learning of calculus, but not as much as I had hoped.

I also bought the Calculus study guide which is a big disappointment. For example, I tried using the integration methods tutor for the integral  cos(5x).

The correct answer is  1/5 sin(5x) + C and is found with U-substitution.

With the tutor, I entered cos5x into the function box.  cos(5x) does not work....

## using integration by parts...

How to solve with maple using integration by parts the integral?int(sec(x)^(n),x);