Posted by Paul on Friday, February 19, 2010 at 3:57am.
well, e^0 is 1
and e^.5 = 1.64
and e^1 is 2.72
so it is a sine wave with increasing amplitude as you approach 1 and frequency increasing with N
The integral of e^ax sin bx dx is
[e^ax/(a^2+b^2)] [a sin bx -b cos bx}here a = 1 and b = N
so
[e^x/(1+N^2)] [sin Nx - N cos Nx]
as N gets big
this looks like
e^x (-N cos Nx)/N^2
or
(-e^x/N)(cos Nx)
e^x is that small constant and cos Nx ranges between -1 and + 1 so as N gets big this goes to zero like 1/N
Now how would you describe the graph of this function when say N=5, N=10, and N=100?
And what does it mean does the graph confirm the limiting behavior of the integral's value?
But how did you arrive at "as N gets big this looks like e^x(-NcosNx)/N^2?????
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