Prove that if T:R^{m} \rightarrow R^{n} and U:R^{n} \rightarrow R^{p} are linear transformations that are both onto, then UT:R^{n} \rightarrow R^{p} is also onto.
Can anyone point me in the right direction? Is there a theorem that I can pull out of the def'n of onto that I can begin this proof?
Suppose in general that we have two functions
F(x)= \int_{0}^{cos x}e^{xt^2} dt
G(x)= \int_{0}^{cos x}\(t^2e^{xt^2} dt
H(x) = G(x) - F'(x)
Where, I need to prove that
H(\frac{\pi}{4}) = e^\frac{\pi}{8}/\sqrt{2}
Okay, so far I have computed the integrals of both of...
I used a table of integrals...and some simple algebra, unless I looked at the wrong intergral form, but I don't think I did, so anyway, where do I use the substitution?
Alright using a table of integrals and some algebra here is what I have so far:
\int_{-\infty}^{\infty}\frac{dt}{(a^2+t^2)^\frac{3}{2}} =
\int_{-\infty}^{\infty}\frac{a}{t^2(a^2+t^2)^\frac{3}{2}} + \frac{3}{t^2}}\int_{-\infty}^{\infty}\frac{dt}{(a^2+t^2)^\frac{1}{2}}
Am I getting...
Can anyone give me any hints as to find a suitable change of variables for this integral.
infinity
/
|dt/(a^2+t^2)^3/2 =
|
/ -infinity
=2/a^2 * integral below...