Recent content by d_b

oh...this is not a homework either, its my exam review questions...

Homework Statement I'm working on this problem but everytime I tried to walk through my answer it doesn't seem right. I wanted to built a ripple counter, up counter with mod 13 using D flip flop. Homework Equations present state ABCD - 0000-->1101 next state ABCD - 0001-->0000...

if I'm not wrong it can't follow because its not a function...I just want to make sure if I got it right

For a sirjective function from A--> B, I was just wondering if more than one elements in B can point to the same element in A if the function is surjective.

For a surjective function from A--> B, I was just wondering if more than one elements in B can point to the same element in A if the function is surjective.

I posted a few of them. Which one are you talking about?

what about y2=U(t)y1 ? Isn't y1 and y2 is the set of fundamental solution?? why is wronskian is not equal to zero then?

For a second order linear differential homogeneous equation, if the two solution y1 and y2 is a multiple of one another. It means that it is linearly dependent which mean they can not form a fundamental set of solutions to second order differential homogeneous equation. Am I correct?? or...

is this the only way of proving \int_{0}^{a} e^{x^2} \,dx

it would be diverge if i was to take from negative infinity or zero to positive infinity. What if i was to take the intergral for a small section. let say from 1 to 5. Would it still be diverge??

(\int_{-\infty}^{\infty}e^{-x^2}dx)^2=(\int_{-\infty}^{\infty}e^{-x^2}dx)\cdot (\int_{-\infty}^{\infty}e^{-y^2}dy)= (\int_{-\infty}^{\infty}e^{-(x^2+y^2)}dxdy)= \int_0^{2\pi}dw\int_0^\infty dr r e^{-r^2}=-\pi e^{-r^2}\vert^\infty_0=\pi THis is what i got...Also would e^x^2 be different...

i found http://en.wikipedia.org/wiki/Gaussian_integral this online which helps...but I was just thinking if i was go havee^{x^2} can i still use the double intergral?? or is there other way of doing it? (ie. using the theory property of exponential)

Thank you for clearing up the problem, I haven't learn how to do double intergral yet so is there any other way of doing it without using double intergral?? also \int_{-\infty}^{\infty} e^{-x^2/2} \,dx = \sqrt{\pi/2}. ...is this correct? what i did i just use e^{-x^2} and substitute -x^2/2...

Think of this function as (x^2 - x^3) and so if you have x to the power of anything will there be a value of x that function f(x) does not exists? ----if there is no value of x that f(x) does not exists then your domain is everything, but if there is a value(s) of x that f(x) does not...

I actually meant to intergrate from negative infinity to positive infinity.