Recent content by Xcron

This next problem is rather strange and it once again involves quadratic factors and I am not able to get the correct answer. The problem is: \int \frac{7x^3-3x^2+73x+53}{(x-1)^2(x^2+25)}dx Step I: 7x^3-3x^2+73x+53 = A(x-1)(x^2+25)+B(x^2+25)+(Cx+D)(x-1)^2 I easily get the value of B by...

Upon further analysis, I realized that the answer is still wrong, this is why: after the division and the a^2 + x^2 trig substitution, the integral is: 2x^2-7x+5\ln|x-3|+ \int\frac{16\tan\theta+24-15}{4\sec^2\theta}2\sec^2\theta d\theta then: x^2-7x+5\ln|x-3|+8\ln|sec\theta|+\frac{9}{2}\theta...

Ok, I just tried that and I finally got the right answer...I guess that's what my error was. After the long division, I need to use the remainder..heh..

Yes, I do have a remainder after I divide. After the long division, I have: 4 x - 7 + \frac{13 x^2 - 69 x + 110}{x^3 - 9 x^2 + 31x - 39} What do I do with it? I was just looking over that because I noticed something about it in the book, but I can't quite grasp what the remainder would be used...

I started this section off quite well and I did very well on the problems where there are only linear factors but when I got to the problems with quadratic factors, I began getting wrong answers. I though that perhaps I would receive some advice or my error/mistake could be corrected if...

Ahhhh, that was my final guess that I was making as to how they would work. It seemed like we weren't supposed to touch/work with x, and thus the main variable that we should be concerned with is n (since that was the target of the limit).

Could you please explain the mechanics of the two variables? I'm not sure how to go about thinking/reasoning the presence of both..

Sorry, I didn't completely specify the directions of the problem. I am required to use L'Hospital's Rule to solve this limit (this is a Calculus class). I was going to us ln y in order to simplify the limit a bit. The definition for the number e is standard I guess...the base of the natural...

Ok, the problem says: Show that \lim_{n\rightarrow\infty} (1+\frac{x}{n})^n = e^x for any x>0.I thought that I could say that y = 1+x/n...and then use the natural logarithm to narrow it down to \ln y=n\ln(\frac{x}{n}) ... I should be getting x so that when I take it back into the original...

I think that for the Midpoint Rule problem...I would have sub-intervals(10) represented by \frac{1}{10}, which would be in front of the Riemann sum. I probably should not use the f(\frac{40.5}{120})...because they seem a bit strange...I'm trying to figure out how to estimate ln 1.5 while doing a...

Ohhhhhh, now I understand. I had understood the part about the 2 points of intersection but was trying to figure out which variable we solve that equation for and I now realize that we find the point on the curve using the intersecting line...which is why we solve for the x in terms of m. I got...

Problem states: (A) Use mathematical induction to prove that for x\geq0 and any positive integer n. e^x\geq1+x+\frac{x^2}{2!}+...+\frac{x^n}{n!} (B) Use part (A) to show that e>2.7. (C) Use part (A) to show that \lim_{x\rightarrow\infty} \frac{e^x}{x^k} =...

Ahh...well, sorry to say this but I am still somewhat confused as to how that equation would be solved...two variables...need to solve for m but that would just give us \frac{1}{x^2+1} ... hmmm...

Can anyone help me with the Midpoint Rule problem...and the new Riemann sum problem please?

Well, from graphing the problem...it seems like y=x may be the right bound of the interval for which y=mx and the curve enclose a region...but I would need to show a calculation for this... I tried: mx= \frac{x}{(x^2+1)} m=\frac{1}{x^2+1} but that only gives me the same equation of the curve...