Well the first one is the same as (sin x)^3(tan4x)</p> So start off with a product rule, and then once you get to the derivative of the first use a chain rule. Remember to put a '4' in front of everything, as that comes from the derivative of 4x once you do the chain rule on the tan term.</p> <hr width="100%" size="2" /> </p> Same as the second one. Start off with a quotient rule, and then chain the denominator once you get there. Remember that the square root is the same as raising something to the (1/2) power. So then when you do the power rule, you'll bring the (1/2) down, subtract 1, and the power will be (-1/2)</p> <hr width="100%" size="2" /> The third one just looks like a pain in the ass chain rule. Just keep plugging along</p> </p>
<div class='quotetop'>QUOTE (GMJigga)</div><div class='quotemain'></p> Well the first one is the same as (sin x)^3(tan4x)</p> So start off with a product rule, and then once you get to the derivative of the first use a chain rule. Remember to put a '4' in front of everything, as that comes from the derivative of 4x once you do the chain rule on the tan term.</p> <hr width="100%" size="2" /> </p> Same as the second one. Start off with a quotient rule, and then chain the denominator once you get there. Remember that the square root is the same as raising something to the (1/2) power. So then when you do the power rule, you'll bring the (1/2) down, subtract 1, and the power will be (-1/2)</p> <hr width="100%" size="2" /> The third one just looks like a pain in the ass chain rule. Just keep plugging along</p> </p> </div></p> The 2nd one doesn't need the quotient rule. Just think of it as 1/3 times (whatever)^(-1/2)</p> </p>
<div class='quotetop'>QUOTE (chingy0007)</div><div class='quotemain'></p> Here's a few for you to try, from my practice British Mathematical Olympiad papers (non-calculator):</p> 1. Let n be an integer greater than 6. Prove that if n-1 and n+1 are both prime, then n^2(n^2+16) is divisible by 720. Is the converse true?</p> 2. Adrian teaches a class of six pairs of twins. He wishes to set up teams for a quiz, but wants to avoid putting any pair of twins into the same team. Subject to this condition: i) In how many ways can he split them into two teams of six? ii) In how many ways can he split them into three teams of four?</p> 3. In the cyclic quadrilateral ABCD, the diagonal AC bisects the angle DAB. The side AD is extended beyond D to a point E. Show that CE=CA if and only if DE=AB.</p> 4. The equilateral triangle ABC has sides of integer length N. The triangle is completely divided (by drawing lines parallel to the sides on the triangle) into equilateral triangular cells of side length 1. A continuous route is chosen, starting inside the cell with vertex A and always crossing from one cell to another through an edge shared by the two cells. No cell is visited more than once. Find, with proof, the greatest number of cells which can be visited.</p> 5. Let G be a convex quadrilateral. Show that there is a point X in the plane of G with the property that every straight line through X divides G into two regions if and only if G is a parallelogram.</p> 6. Let T be a set of 2005 coplanar points with no three collinear. Show that, for any of the 2005 points, the number of triangles it lies strictly within, whose vertices are points in T, is even.</p> That is one full paper, that you get 3 1/2 hours to do. We were told that we would be doing very well if we manage to answer 2.</p> Two more from another paper:</p> 1. Find four prime numbers less than 100 which are factors of 3^32 - 2^32.</p> 3. The number 916238457 is an example of a nine-digit number which contains each of the digits 1 to 9 exactly once. It also has the property that the digits 1 to 5 occur in their natural order, while the digits 1 to 6 do not. How many such numbers are there?</p> </div></p> I feel like I could do 1 from the first one, and the last 2. But that's just a hunch.</p> Anybody seen the Joy of Mathematics DVD's?</p> </p>
Actually, no its not. if you separate the 3 out you're still left with 1 over the denominator. You could do the quotient rule, or use a chain rule if you convert 1/ denom to denom^-1</p>
doing a 4000 word Essay on how the Communist Governments maintained control over the Eastern states. Not really Stuck on it just thought i'd mention it. I've decided that instead of Cramming it for 2-3 hours i'd rather take 4-5 hours and put the odd post on here to Cool my brain down</p>
I'd rather do essays than math problems, at this point. Always felt that way, too. Why did I go into computer science again?</p>
A circle of radius 2 and center (0,0) can be parametrized by the equations x = 2 cost t and y = 2 sin t. Show that for any value t, the line tangent to the circle at (2 cos t, 2 sin t) is perpendicular to the radius.</p> How the hell do you prove that?</p>
not sure what parametrized means (perhaps that those equations form part of the circle?)</p> The line perp. to the radius is the derivative, so I would try finding the deriviative to each equation and seeing where you go from there</p>
<div class='quotetop'>QUOTE (GMJigga)</div><div class='quotemain'></p> not sure what parametrized means (perhaps that those equations form part of the circle?)</p> The line perp. to the radius is the derivative, so I would try finding the deriviative to each equation and seeing where you go from there</p> </div></p> Parametrized means that the function has a parameter, which is time. (t).</p> I'll try that, that assignment is like a week and a half late now.</p> </p>
Oh, as in 0<t<=x?</p> Reading it again, I think the key is the point they give you the point (2 cos t, 2 sin t).</p> The derivative will be perpendicular to the radius, if it lies on the circle (definition of circle, and derivative)</p> So you have to prove that the point is on the circle within 0<t<=x</p> So take the derivative of the cos and sin functions. They should equal each other. Boom; proved</p> edit: to prove equality use x=2</p>
Parametrization is another way of defining a graph- especially one that can't be defined as a function (the way that a circle isn't really a function, since you have two y's for each x). It's kind of weird to go from the chain rule to parametrization- what class is this?</p> The slope of the tangent line is dy/dt over dx/dt which I assume you already know. Once you get the slope, all you have to do is show that this is the negative reciprocal of the slope of the radius, right?</p>
<div class='quotetop'>QUOTE (lukewarmplay)</div><div class='quotemain'></p> Once you get the slope, all you have to do is show that this is the negative reciprocal of the slope of the radius, right?</p> </div></p> Good call. You can find the slope by using (2, 2cos(s)), and (0,0) as the other point</p> </p>
<div class='quotetop'>QUOTE (Master Shake)</div><div class='quotemain'></p> I'll start helping in this thread when you guys have questions about sex ed.</p> </div></p> </p> Which hole?</p> Why am I even asking, I KNOW the answer is the butthole.</p> </p>
<div class='quotetop'>QUOTE (Kid Chocolate)</div><div class='quotemain'></p> <div class='quotetop'>QUOTE (Master Shake)</div><div class='quotemain'></p> I'll start helping in this thread when you guys have questions about sex ed.</p> </div></p> </p> Which hole?</p> Why am I even asking, I KNOW the answer is the butthole.</p> </p> </div></p> </p> If you're Greek, then yes. If you aren't, then maybe not.</p>
<div class='quotetop'>QUOTE (Kid Chocolate)</div><div class='quotemain'></p> Why am I even asking, I KNOW the answer is the butthole.</p> </p> </div></p> That's the safe guess, like picking 'C' on a multiple choice exam</p> </p>
I have this problem....</p> </p> Let f(x)= cos x + 3x</p> Show that f has a differentiable inverse</p> Find f(0) and f ' (0)</p> Find f^-1 (1) and (f^-1)'(1)</p> For part c, what is that? Is that just making the cos, into cos^-1 x ???</p>
