<p>Rules: Simple, answer a question or ask a question. Make sure most if not all questions get answered.</p>
<p>NOTE: IF YOU ARE ASKING A QUESTION, PLEASE HAVE THE ANSWER ON YOU. </p>
<p>edit = I'll be monitoring this thread frequently. I'll try to answer as many as I can. </p>
<p>::::::::BEGIN::::::::::</p>
<p>I'll start...</p>
<p>Integration{e^(x) * cos[x]} = ?</p>
<p>edit: try not to use a calculator...</p>
<p>Solution:</p>
<p>[ ( e^x * sin(x) ) + ( e^x * cos(x) ) ] /2 + C</p>
<p>Done in 1 min give or take a few secs.<br>
Done using uv - integral of v du, aka integration by parts.</p>
<p>EDIT = Whoops. Forgot the Integration constant, C.</p>
<p>New problem:</p>
<p>lim x-> 0 of sin(x)/x</p>
<p>HAHA RESMonkey, you can do better than that...your q is a joke..</p>
<p>its a constant rule (im x-> 0 of sin(x)/x always equals 1) there's another one for cosine
also you can use lhopital's rule, it becomes cos(x) / 1, so cos(0) = 1</p>
<p>New problem:</p>
<p>here's a tough one, just for you monkey...</p>
<p>Integration {dx / sqrt[4 - x^2]}, limits of integration are 1, 2</p>
<p>sqrt = square root
REMEMBER NO CALCULATOR!!!! lol...</p>
<p>That's easier than my general rule one. Just factor out 4, grab it outta the square to make it a 2, and you can recognize it as arcsine function:</p>
<p>arcsin(x/2) +C</p>
<p>New prob....</p>
<p>Summtion (sigma symbol), n=1, n goes to infinity, :</p>
<p>((-1)^n * 3^n ) / ( n * 2^n)</p>
<p>Converges or diverges? State what method used.</p>
<p>AAAAAHHHHH you have discovered my weakness RESmonkey, NOOOOOOOO</p>
<p>let me try it:</p>
<p>ok, so ratio test yields -1.5, so since the limit < 1, the series converges...</p>
<p>new prob...</p>
<p>*) The horizontal asymptotes of ƒ(x) = { (1 - |x|) / x } are given by?</p>
<p>explain your reasoning...or not...lol..</p>
<p>Actually, I believe that series diverges. Try the alternating series test before you jump to ratio. I'll do your problem in just a sec.</p>
<p>edit = I see what you did. You forgot the absolute value around -1.5. 1.5 > 1, therefore diverges. I guess you could have done ratio from the start.</p>
<p>Are there no horizontal asymptotes? Some how, it turns into a vertical instead of a hole. </p>
<p>Is there more to this?</p>
<p>l i m { (1 - |x|) / x } = l i m { (1 - x) / x } = -1 (L'Hopital)
x --> infinity x --> infinity</p>
<p>l i m { (1 - |x|) / x } = l i m { (1 + x) / x } = 1 (L'Hopital)
x --> - infinity x --> - infinity</p>
<p>The horizontal asymptotes of { (1 - |x|) / x } are y= 1 and y = -1</p>
<p>Next Question:</p>
<p>Find the volume of the solid generated by revolving the given region bounded by the given lines and curves around the x-axis:</p>
<p>y = x^2, y=0, x=2</p>
<p>easy! </p>
<p>integrate from 0 to 2, x^2 dx
so
8/3 is the answer to previous</p>
<p>Next question: WORK/pumping water!</p>
<p>An open tank has the shape of a right circular cone. The tank is 8 feet across the top and 6 feet high. How much work is done in emptying the tank by pumping the water over the top edge. </p>
<p>This one is a little tricky and not easy (: I'll check back tomorrow after school to see if someone has solved it.</p>
<p>WantIvy:</p>
<p>Your answer gives the area under the curve, but not the volume if that area were rotated about the x-axis.</p>
<p>My question is still open.</p>
<p>@diamondbacker's q:</p>
<p>integrate from 0 to 2, of (x^2)^2 dx * pi = 32*pi/5</p>
<p>Pi * Integration of x^4 from 0 to 2 is the answer for diamondbacker's.</p>
<p>vader, Make sure you read why my problem diverages, omitance of abs. value is a dangerous thing :P</p>
<p>Want Ivy:</p>
<p>Umm...are you sure that's Calc BC? </p>
<p>Heres my take at it:</p>
<p>Work (from Physics) = Fdcos(theta). </p>
<p>Dunno where or how to apply this. I'll post again in 10 mins with more thought into it.</p>
<p>I googled; </p>
<p>Work = integrate [ density of water (1?) * gravity (9.8) * Pi *radius squared( 4^2?) * y ] dy from 0 to 6.</p>
<p>That's definitely not Calculus BC, more like college Calc/Physics with calc??</p>
<p>Yeah, thanks a lot RESmonkey for that absolute value thing...I made the same mistake last week on my quiz in calc class (got a 9/10 on it though...)</p>