Homework Statement
Find the absolute extrema of f(x) = e^-x * ln(lnx)
The Attempt at a Solution
Ive successfully taken the first derivative and set it to zero. The problem is checking the sign of 1/(xlnx) - ln(lnx)
No matter how I try to manipulate this, I cant seem to isolate x. Its...
Thats a good one (with nice geometer's sketchpad potential), but someone else is already doing it. So far, Ive found this:
Two poles, one 6 meters tall and one 15 meters tall, are 20 meters apart. A length of wire is attached to the top of each pole and it is also staked to the ground...
For a calc project, I am supposed to solve an interesting calculus word problem dealing with maximum and minimum values. The catch is that I cannot use my own book. Can anyone suggest a challenging optimization problem? So far, weve covered the problem with a person who must find the least time...
Im in pretty much the same situation, and it seems like the answer is electrical engineering. There are opportunities to specialize in signal processing, for example, at the grad level
Horizontal plane.
For anyone interested, I looked up the solutions, and they were able to simplify it greatly with the small angle approximations sin(theta)=theta and cos(theta)=1
Then the torque is -kL2theta, the acceleration is k/[2m]. Then they solved it in one magic step to get...
Homework Statement
A stick of length 2L and negligible mass has a point mass m affixed to each end. The stick is arranged so that it pivots in a horizontal plane about a frictionless vertical axis through its center. A spring of force constant k is connected to one of the masses. The system...
You can calculate the product of the masses with the given force and distance. Then because you know the sum, you have a system of 2 equations with 2 unknowns
Homework Statement
A freight elevator weighing 3000 pounds is supported by a 12 foot long cable that weighs 14 pounds per linear foot. Approximate the work required to lift the elevator 9 feet by winding the cable onto a winch
Homework Equations
W = int(f)dy
The Attempt at a Solution
The...
No, the negative is correct. In a related rates problem, negatives are very important. If dD/dt wound up negative, the distance would be decreasing
The only thing I can think of is that your book may want the magnitude of the particle's velocity. dx/dt is the horizontal component and dy/dt is...
The trick is to pick a temporary delta neighborhood (remember your temporary delta) and bound your function. Bound the numerator and denominator separately, remembering the archemidian principle for the denominator. Youll come up delta being less than epsilon times a coefficient as usual. But...
With calculus you can show that the given line and the line tangent to the circle at the single intersection point are one and the same. But all you need to do is prove that there is only one intersection
For an angle in standard position (between the x axis and force vector), sine will give the y component and cosine will give the x component. You have to be careful if the question says something like "20 degrees west of north", but here they state each angle is in standard position
APB is more general and covers many more areas like thermo, nuclear physics, and optics. None of it is too challenging, but its probably not in your textbook. APC goes very in depth on two subjects: mechanics and E&M. If you dont want to buy another textbook, you should get some sort of AP guide...
The APC exams test your knowledge of physics, not calculus. If youre motivated, youll be able to do well on the mechanics exam with little calc background.
BTW theres no need to take math 1 and 2 SATIIs. Its typically one or the other. Math 2 usually has a fair amount of trig. When colleges say...
I wouldnt try the Calc BC exam this year with no knowledge of precalc (exponential and trigonometric functions). Try to get into a precalc class to prepare you for next year. If you feel ambitious, start to look up the beginnings of limits and derivatives on your own, but dont take a whole class
The two objects rotate around the center of mass of the system. In this case, the objects have the same mass so the COM is at the geometric center of the system. r doesnt equal the seperation distance, but the distance from the center of mass of the system