Recent content by InaudibleTree

Ok, great! Thank you soroban.

An academic department with five faculty members narrowed its choice for department head to either candidate A or candidate B. Each member then voted on a slip of paper for one of the candidates. Suppose there are actually three votes for A and two for B. If the slips are selected for tallying...

Homework Statement F(x) = \int^{ln(x)}_{\pi}cos(e^t)\,dt Homework Equations The Attempt at a Solution Following from a theorem given in the text I am using: If f is continuous on an open interval I containing a, then, for every x in the interval, d/dx[\int^x_af(t)\,dt] = f(x) I thought it...

Oh ok. Thank you curious.

Homework Statement \int1/(1+\sqrt{2x})\,dx Homework Equations u=1+\sqrt{2x} \Rightarrow \sqrt{2x}=u-1 du=1/\sqrt{2x}dx \Rightarrow \sqrt{2x}du=dxThe Attempt at a Solution \int1/(1+\sqrt{2x})\,dx = \int\sqrt{2x}/(1+\sqrt{2x})\,du = \int(u-1)/u\,du = \int\,du-\int1/u\,du = u-ln|u|+C =...

Oh right. I see the mistake I made. Thanks qbert. But I still don't see how that leads to \int^0_{-a}f(x)\,dx = \int^a_0f(x)\,dx I was looing at it as if the author was using a theorem he proved earlier in the text: If u=g(x) has a continuous derivative on the closed interval [a,b] and...

Homework Statement Let f be integrable on the closed interval [-a,a] If f is an even function, then \int^a_{-a}f(x)\,dx = 2\int^a_0f(x)\,dx Prove this. Homework Equations The Attempt at a Solution The solution is given in the book. Because f is even, you know that f(x) =...

Im sorry I should of structured my post better. I knew the inequality given was established earlier in the proof. I reread the definition of infinite limits. I think what you are saying makes sense. Im really just allowed to choose an M>0(in this case M -L + 1) and at some point(s) f(x) >...

Assume for some real number L and c \displaystyle\lim_{x\rightarrow c} f(x) = ∞ and \displaystyle\lim_{x\rightarrow c} g(x) = L We must prove \displaystyle\lim_{x\rightarrow c} [f(x) + g(x)] = ∞ Let M > 0. We know \displaystyle\lim_{x\rightarrow c} f(x) = ∞. Thus, there exists...