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**mrpace**- Replies: 0

determine the laplace transform of f(t) of the following

f(t) =

e^(-t) when 0 ≤ t ≤ 5

-1 when t > 5

I got my answer as simply 1/(s+1) when 0 ≤ s ≤ 5

-1/s when s > 5

I'm not sure if this is right though.

**mrpace**- Replies: 1

Find all real values of a and b such that the following is a reflection

T: X = aX + (24/25)Y

Y bY + (24/25)X

Sorry for the lack of latex; I'm sure you can work it out.

Agnishom wrote:

There is no need to factor it. You are confusing yourself by factoring it

Really? I'm trying with it not factored and not having any luck.. can you help?

**mrpace**- Replies: 3

show, using the formal definition of a limit, that:

lim

x^2=4

x -> 2

I'm getting to a point where I have |x+2||x-2| < E

But I don't know where to go from there. Help is much appreciated.

**mrpace**- Replies: 1

Find a sequence of plane rotations that transform x = [6 6 17] to a multiple of [1 0 0].

Any ideas??

**mrpace**- Replies: 3

Show that if A and B represent reflections in R3, then AB represents a rotation in R3.

Any help is appreciated.

**mrpace**- Replies: 1

A force of 400 N stretches a spring 2 meters. A mass of 50 kg is attached to the

end of the spring and is initially released from the equilibrium position with an

upward velocity of 10 m/s. Find the equation of motion

My answer is x=5sin(2t)

If youu get something different, can you show me how you got it please?

Cheers.

**mrpace**- Replies: 2

Find a general solution to

y′′′ − y′′ + 2y = 0

I have never dealt with 3rd order D.E before. I hope you have!

**mrpace**- Replies: 1

Given that y1 = x^(-2) , find a second linearly independent solution to

(x^2)y′′ + 6xy′ + 6y = 0, x > 0.

Any help would be much appreciated.

Hey that's really nice. Just one thing. How would you say in English min{d1,d2,d}?

and i see where the d1 and d2 come from in the brakets above, but where does the d come from??

d=delta obv.

**mrpace**- Replies: 3

Prove that if lim f(x) = lim g(x) = b, and if there exists a number δ > 0 such that...

x→a x→a

0 < |x − a| < δ ⇒ f(x) ≤ h(x) ≤ g(x)

then lim h(x) = b.

x→a

Worked on this for a while without getting anywhere. Any ideas???

**mrpace**- Replies: 8

If f(x) = ax + b for all real numbers x, where a and b are numbers, find for what values

of a and b is it true that ff = f o f?

Not sure what it means by ff or f o f. Help is much appreciated.

bob bundy wrote:

hi mrpace

Because the definition comes in two parts, the answer will too.

x ≥ 0 :

x < 0

You could argue that f(0) is undefined when x < 1 and therefore this second answer cannot be determined but I don't think that is intended.

I have used Latex. If you click on the expression above you'll get a window that shows the code for this. You have to add at the start square brackets math, and complete the code with square brackets /math

Thus:

`[math]\frac{h^2 - 0}{h} = \frac{h^2}{h} = h[/math]`

There's a tutorial to get you started here:

http://www.mathisfunforum.com/viewtopic.php?id=4397

The first few posts in that thread will be enough to get you started. There's an editor at:

http://latex.codecogs.com/eqneditor/editor.php

Bob

Great. I see how it works now. Thanks a lot.

**mrpace**- Replies: 2

If f(x) = x^2 if x is greater than or equal to zero.

= 1 if x is less than zero

then find an expression for the following:

[f(h) - f(0)] / h

h can't equal zero obviously

I don't know how to do these problems so any help is appreciated.

Sorry for the lack of latex...i tried to learn but i don't get it.

**mrpace**- Replies: 1

u = [i, 2i]

v = [2-i, 1+i]

find |u| and |v|

Not sure on this.

**mrpace**- Replies: 1

Let T : V --> W be a linear transformation with ker(T) = {0}

Suppose u1, u2 ∈ V are linearly independent.

Prove that T(u1) and T(u2) are linearly independent vectors in W.

Just not sure how to construct this. Any help would be great, thanks.

bobbym wrote:

Use codecogs, I sent you the link already.

cool, thanks. Are you able to help me with this question?

**mrpace**- Replies: 2

dy + y³x+y=0

dx

solve

Looks innocent but I can't figure.

Sorry for all the DE questions, I have a russian lecturer who I can't understand so I need to learn somewhere

bobbym wrote:

Hi;

Is this what you want?

or

with y(1)=1?

the 2nd one sorry. I don't know how you do those nice symbols haha.

bobbym wrote:

Integrate both sides which will eliminate the differentials dx and dy.

Thanks a lot. Would you be able to help me with my initial value problem that i just posted?

**mrpace**- Replies: 5

dy + 3y + 2 = 3x , y(1)=1

dx x

Not sure how to go about this one.

**mrpace**- Replies: 1

Integrate dx or 1 *dx

xcos(v) xcos(v)

any idea?

bobbym wrote:

The DE is separable:

Now can you integrate both sides?

Ok so what does it mean by solving explicitly for the y differential equation? do i only intergrate the side with the y or what?

**mrpace**- Replies: 5

Solve explicitly for the y differential equation.

dy = 3x^2(1+y^2)

dx

I don't really know what this means. Any help means a lot.

**mrpace**- Replies: 6

n+1

(-1 )^(n-1) * 2n+1

what happens as n goes to infinity?

My thoughts are that it oscillates between near 0.5 and -0.5 but never hits either. does this mean it diverges?