Explore BrainMass



Please show how to solve to the answer of 1/2 If f(x) = x-1/x +1 for all x not equal to -1, then f'(1) =

Differentiation: Increase in height of sand pile with volume

At a sand and gravel plant, sand is falling off a conveyor and onto a conical pile at a rate of 10 cubic feet per minute. The diameter of the base of the cone is approximately 3x the altitude. At what rate is the height of the pile changing when the pile is 15 feet high?

Equation describing the motion of a buoy

Please explain how to solve to the following problem: A buoy oscillates in simple harmonic motion y = A cos omega(t) The buoy moves a total of 3.5 feet (vertically) from its low point to its high point. It returns to its high point every 10 seconds. (a) Write an equation describing the motion of the buoy if it is at its

Related Rates : Application of Derivatives Word Problems

2 (a) If A is the area of a circle with radius r and the circle expands as time passes, find dA/dt in terms of dr/dt (b) Suppose oil spills from a ruptured tanker and spreads in a circular pattern. If the radius of the oil spill increases at a constant rate of 1m/s how fast is the area of the spill increasing when the radius


Differentiate: 1) y=(cos(x)^cot^2(x) 2) find the second derivative of sin(x^2*y)=-cos(x^2*y) note: *=multiply


The curve y = ax2(ax sqaured) + bx passes through the point (2, 4) with gradient 8. Find a and b I have the answer but do not understand how to get to it. Therefore, could you please show full workings. Many thanks.

Derivatives and Graphing : Local Maxima and Minima and Sketching Graphs

The function has a derivative everywhere and has just one critical point, . In parts (a)-(d), you are given additional conditions. In each case decide whether is a local maximum, a local minimum, or neither. Explain your reasoning. Sketch possible graphs for all four cases. a) b) c) d) Please see th

Application of Derivatives Word Problem : Future Value of Investment

Assume that you collect P dollars from a transaction and being a mathematics wiz, you have developed formula to calculate the future value of your investment: where, r is the rate of interest and t is the time horizon. Suppose you invest your profit, P dollars, from above transaction, and invest it in a bank at 5% rate of

Linear Isometry, Radon-Nikodym Derivative and Isomorphisms

Let be a measurable space and let be two -finite measures defined on . Suppose and is the Radon-Nikodym derivative of with respect to . Define by Show that is a well-defined linear isometry and is an isomorphism if and only if (i.e are mutually absolutely continuous). ---


I am not sure how to set up this problem, I think that I have to use the exponential rule, but after that I am lost. (See attached file for full problem description with complete equations) --- The quantity q, of a certain skateboard sold depends on the selling price, p, in dollars, so, we write q = f(p). You are give