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...
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...
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...
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...
Homework Statement
Consider a particle along a curve C and whose position is given by the vector:
s(t) = < sqrt(t2), t3 - 3t >
Last part of the question:
There is an unknown force that is keeping this particle on trajectory C. At what value of t must the force cease in order for the...
Homework Statement
Im not good with latex, but Im having trouble with the limit as x approaches -1 of
[sin(x2+3x+2)]/(x3+1)
The Attempt at a Solution
Ive tried substituting u = x2+3x+2 but I keep getting -1/4 instead of the correct limit 1/3
by long division, x3+1 = (x2+3x+2)(x-3) +...
This was taken from a math contest a few months ago.
Homework Statement
xx*yy=zz
find z if:
x=28 * 38
y=212 * 36
Homework Equations
Theres undoubtably some trick, but I have yet to find it
The Attempt at a Solution
Dont even think about calculator
I showed my math teacher, and...
Homework Statement
One of the beams of an interferometer passes through a small glass container containing a cavity 1.30 cm deep. When a gas is allowed to slowly fill thr container, a total of 236 dark fringes are counted to move past a reference line. The light used has a wavelength of 610...
The last step in a problem of mine is to find all solutions between 0 and pi/2 of the following equation:
R(tanx + 1/cosx + x - 1) = 1/2R2(tanx - x)
By simple inspection and with the aid of a graphing calculator, its obvious that the only solution is x=0, regardless of the value of R. This is...
Homework Statement
Ive got a question regarding a recent AP free response, http://www.collegeboard.com/prod_downloads/ap/students/physics/b_physics_b_frq_03.pdf
Problem 5 is about a simple refrigerator, work is applied and heat is removed keeping temperature constant.
My question is on...
I need to give examples of an instance in which temperature remains constant when heat flows in and out of a system, isothermal by definition. I know the textbook example (slowly heating an ideal gas in a cylinder with a piston on one end, volume increases as pressure decreases, etc.), but are...
Homework Statement
A uniform rod of mass M and length L is free to rotate about a horizontal axis perpendicular to the rod and through one end. A) Find the period of oscillation for small angular displacements. B) Find the period if the axis is a distance x from the center of mass
Homework...
Homework Statement
A block attached to a spring underneath oscillates vertically with a frequency of 4Hz and an amplitude of 7.00cm. A tiny bead is placed on top of the block jut as it reaches its lowest point. Assume the bead's mass is so small that its effect on the motion of the block is...
I just want to quickly check something. A spring scale lies horizontally on a frictionless surface. A horizontal force of 10 N to the right is applied to the top of the scale and another horizontal force of 10 N to the left is applied to the bottom.
1. The net force is ___ obviously 20 N...
A small block of mass m is on a horizontal frictionless surface as it travels around the inside of a hoop of radius R. The coefficient of friction between the block and the wall is mu; therefore, the speed v of the block decreases. In terms of m, R, mu, and v, find expressions for:
a. the...