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...
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...
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...
For #4, the derivative is a quadratic. There are 2 places where the tan line has a slope of 5. Find the points where it equals 5 (or where that minus 5 equals zero) and then you have 2 points and 2 slopes
Thanks for the explainations. Im not afraid of LHospitals rule, but we just finished trig limits and are just starting derivatives. Needless to say, we havent gone over it formally in class. The problem was given in a section of the book before LHospitals rule, so I wanted to know how it could...
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) +...