Square Wave Form Differentiation

[spacekeys]

Plot this function from t=0 to t=0.1 and determine where this function x(t) is differentiable.

X(t) = 1+(4/pi)(sin(2pi50t)+(1/3)sin(6pi50t)+(1/5)sin(10pi50t))

I have entered the equation into WolframAlpha. Can somebody help me determine where this function is differentiable?

http://www.wolframalpha.com/input/?...in(6pi50t)+(1/5)sin(10pi50t))+from+t=0+to+0.1

Also, find the square wave function that x(t) approximates.

 

[Deleted member 4993]

Plot this function from t=0 to t=0.1 and determine where this function x(t) is differentiable.

X(t) = 1+(4/pi)(sin(2pi50t)+(1/3)sin(6pi50t)+(1/5)sin(10pi50t))

I have entered the equation into WolframAlpha. Can somebody help me determine where this function is differentiable?

http://www.wolframalpha.com/input/?...in(6pi50t)+(1/5)sin(10pi50t))+from+t=0+to+0.1

Also, find the square wave function that x(t) approximates.

do you know of any point where y = sin(x) is not differentiable?

 

[Ishuda]

...Also, find the square wave function that x(t) approximates.

Do you know what a square wave is?
http://tinyurl.com/oy7jsnk

 

[spacekeys]

Do you know what a square wave is?
http://tinyurl.com/oy7jsnk

This is what I believe the problem is asking for.

http://en.wikipedia.org/wiki/File:SquareWave.gif

 

[spacekeys]

Do you know what a square wave is?
http://tinyurl.com/oy7jsnk

I believe this is similar to what it is looking for. http://en.wikipedia.org/wiki/File:SquareWave.gif

 

[spacekeys]

do you know of any point where y = sin(x) is not differentiable?

No, there isn't any point on y = sin(x) that is not differentiable right? Does that mean that the function I was given is differentiable everywhere?

 

[Deleted member 4993]

No, there isn't any point on y = sin(x) that is not differentiable right? Does that mean that the function I was given is differentiable everywhere?

You make that decision from your knowledge of "definition of differentiability".

 

[spacekeys]

You make that decision from your knowledge of "definition of differentiability".

That is why I posted this question, because I needed help with that decision. I don't understand the definition perfectly. I understand it enough to know that sin(x) is differentiable everywhere, but I am unsure about the function I was given. That is why I posted this thread.

 

[HallsofIvy]

For a function of one variable, f(x), "differentiable at x= a" means that the derivative exists at x= a, which means that $\displaystyle \lim_{h\to 0}\frac{f(a+ h)- f(a)}{h}$ exists.

 

[Ishuda]

...X(t) = 1+(4/pi)(sin(2pi50t)+(1/3)sin(6pi50t)+(1/5)sin(10pi50t))

I have entered the equation into WolframAlpha. Can somebody help me determine where this function is differentiable?...

We know sin (x) is differentiable with respect to (wrt) x as is sin(t) wrt t, sin (z) wrt z, etc. Is sin(2 $\displaystyle \pi$ 50 t) differentiable wrt t? Yes, just let x = 2 $\displaystyle \pi$ 50 t and we have sin(x) which is differentiable wrt x and, since x is differentiable wrt t, by the chain rule we have sin(x) is differentiable wrt t.