Recent content by Dr. Lady

Homework Statement Let f(x,y)= 1 if x is rational, 2*y if x is irrational Compute both double integrals of f(x,y) over [0,1]x[0,1] Homework Equations The Attempt at a Solution I'm tempted to say that we can do the dydx integral since when x is rational, integrating y gives...

http://en.wikipedia.org/wiki/Total_monotonicity If a function is strictly decreasing, then it's monotonically decreasing. Which then means that it's a total monotone by the definition in the link above.

Well, it looks like you can take 10^ of each side... see where that gets you.

Sure... but you can't always rely on guess and check. In this problem we see that there's a principal, a rate, and an interest. We need a problem that accomadates them and only them, and we happen to have P*r=I, which we just need to modify for our uses. Word problems are almost always best...

Think trig identities...

There's a much easier way to do it with one equation and no proportions. Practice makes word problems easier! .03*x+.05*(6000-x)=220

It's a constant, and d(c*f(x))/dx=c*d(f(x))/dx As an example, the derivative of 2x is 2. Nothing changes about that when you do trig.

You should check you're algebra in your equation... which should have a limit, of course.

I don't see any problem. You should be familiar with a method of integration called u-substitution that would do the trick. If you're in a Calc I class, then you might learn this soon.

The answer should be infinity, even without l'Hospital's, simply by virtue of the quadratic in the numerator. Check to you have the right equation or right way of checking the answer.

'Tis true... both of the above.

Think of it as multiplying the the dt over to the other side, and then dividing the v the other way. So we have. -\lambdadt=m*dv/v Now integrate both sides, one is an integral of dt the other dv. Mathematically, this is not exactly what's going on, but you'll learn more when you take a...

I can't think of any way to do this pre-calculus, but I can guarantee that you could do it with calculus. Take circular slices of the solid going along the radius pointing toward the center of the large sphere, find an equation for the Area of the circles based on how far you are along the...

The integral of x^-1 is ln(x)... taken at the limits given, that's not infinity. You're method for solving is sound, but x^-1 is just one that you have to memorize.

However, if finding a fraction, regardless of rationality is what you want, you can do this. Remember that a square root can also be described as an exponent of 1/2. And like other exponents, it can be 'distributed' to each number that is being multiplied or divided. Of course, if you can...