<p>how many questions will they repeat on the multiple choice from last 2 to 3 years?</p>
<p>bump, any one</p>
<p>Find the derivative of f(x) = x^x.</p>
<p>Collegeboard.com:
[quote]
Appropriate integrals are used in a variety of applications to model physical, social, or economic situations. ... Whatever applications are chosen, the emphasis is on using the method of setting up an approximating Riemann sum and representing its limit as a definite integral. To provide a common foundation, specific applications should include finding the area of a region (including a region bounded by polar curves), the volume of a solid with known cross sections, the average value of a function, the distance traveled by a particle along a line, and for BC only the length of a curve (including a curve given in parametric form).
[/quote]
</p>
<p>Work problems aren't specifically listed in the topic outline, but I think they are fair game. In doing past questions though, I don't think I've seen any really hard ones. </p>
<p>NEWTON'S METHOD
is used to approximate roots by "guessing" values on either side of it and then zooming in from both sides... this is how your calculator finds zeroes from graphs</p>
<p>Newton Recursive Formula (for manually doing this):
x<em>o= guess for root (seed value)
x</em>n= x<em>n-1 - f(x</em>n-1)/f'(x_n-1) for n greater than or equal to 1</p>
<p>x_o is x sub-zero</p>
<p>go on AIM's room: apcalcbc to chat and do questions.</p>
<p>
[quote]
f(x) = x^x.
[/quote]
dy/dx=x^x + (x^x)lnx</p>
<p>I don't know the answer but I'm pretty sure you're wrong noober.</p>
<p>Noober is correct.</p>
<p>isn't it (x^x)ln(x+1)?</p>
<p>It's x^x(lnx + 1).</p>
<p>
[quote]
I don't know the answer but I'm pretty sure you're wrong noober.
[/quote]
y=x^x
lny = xlnx
dy/y = x/x<em>dx + lnx</em>dx
dy/y = dx(1+lnx)
dy/dx = y(1+lnx)
Substituting y=x^x, dy/dx = x^x(1+lnx) = x^x +(x^x)lnx</p>
<p>The rate that an object cools is directly proportional to the difference between its temperature (in Kelvins) at that time and the surrounding temperature (in Kelvins). If an object is initially at 35*K*, and the surrounding temperature remains constant at 10*K*, it takes 5 minutes for the object to cool to 25*K*. How long will it take for the object to cool to 20*K*?</p>
<p>Newton's Law of Cooling won't be on it, right?</p>
<p>I don't think so. That problem is a differential equation.</p>
<p>what programs do u think would be useful to have on our calculator for the test?</p>
<p>What do we have to know about error for series (besides lagrange)? Do we have to know the remainder formulas? Also, do we need to know the error bounds for the trapezoidal rule for integrals?</p>
<p>I have a question:</p>
<p>What are the points of inflection of f(x)=3x^5-5x^4</p>
<p>I took the second derivative and thought the answer was 0 and 1 but according to the 98 ap test it is 1. anyone care to explain? thanks.</p>
<p>dy/dx = 15x^4 - 20x^3
d2y/dx2 = 60x^3 - 60x^2 = 0
60x^2(x-1)=0, x=0,1
<---0---1--->
....-....-....+
2nd Derivative changes sign at 1, so it's a point of inflection. It doesn't at 0 because there's no sign change.</p>
<p>f(x) = 3x^5 - 5x^4
f'(x) = 15x^4 - 20x^3
f''(x) = 60x^3 - 60x^2
Set f''(x) equal to 0.
60x^3 - 60x^2 = 0.
60x^2(x - 1) = 0.
Right now, we see that x can equal either 0 or 1. We need to check that 0 and 1 are actually both points of inflection.
To check 0, use the points x = -1 and x = 0.8 [using x = 1 will just yield 0] to see if the sign of f''(x) changes.
f''(x) = 60x^3 - 60x^2
f''(-1) = 60(-1)^3 - 60(-1)^2 = -120.
f''(.8) = 60(.8)^3 - 60(.8)^2 = -7.68.
The sign does not change. Therefore, 0 is not a point of inflection. If you repeat the same with x = 1, you'll see that the sign does change, meaning the concavity changes, while implies that x = 1 is a point of inflection.</p>
<p>I have a question:</p>
<p>what is value of sum from n=1 to infinity of (2^(n+1))/(3^n)</p>
<p>please show steps also</p>
<p>ok this is easy...its geometric meaning that it is essentially the sum from one to infinity of 2 times (2/3)^n. Because the summation of geometric series is a/(1-r), you get 6. But don't stop there. That formula only applies when its from 0 to infinity so subtract the 0 term from 6, which is 2. So the answer is 4</p>