Toddio

An equation such as: (x^2 - 6x + 1)^(5/3) = -32

can be solved by raising both sides to the "3/5's" power.

Let's call this method, "raising to the reciprocal power"

This method can produce extraneous solutions.

For a quadratic under the rational exponent it can produce:

A) Two real solutions (like the above)

B) No real solutions (i.e. 2 complex solutions similar to the above)

Under what conditions will the method produce two "possible" real solutions with one being valid and the other being extraneous???

An example would be okay, but conditions on the equation would be better.

Thanks in advance.

Show that any polynomial that includes at least one even-powered term and at least one odd-powered term, is neither odd nor even.

If you want use the simplest case of:

P(x) = ax^n + bx^m + ...

Where a and b are real and not equal to zero, n is even and not equal to zero and m is odd...

If you purport that this statement is not true, provide a counter-example.

Thanks in advance.

Would someone please indicate a link that outlines the umbra and penumbra for the upcoming eclipse on the surface of the earth or a map of the world?

I am not finding this anywhere.

If I am in partiality, I will take some astrophotos.

Thanks in advance!

Is it cheating to put a word or phrase for an answer so as to be the first answerer, then use "edit" to add a real answer, again just to get to be first on the list?

I have seen others doing it and it doesn't seem appropriate.

Most people who add to or change an answer, note it with "edit" or some other phrase.

What do you think?

Anyone know of a link, links or other document that provides something of an algorithm for determining the best methods of integration for a given function. Beyond a list of techniques, more an algorithm for selecting techniques. (for example, "when integrating a product of a trig function and a polynomial, use integration by parts setting the polynomial = to u."

Any resources would be helpful.

Thank you all in advance.

What is the domain of this REAL function?

f(x) = (4x/3)((x^2 - 1)^(-1/3))

I get |x|>1

Does this look right?

Question is as follows:

What is the maximum surface area of the curved surface of a cylinder inscribed in a sphere of radius R. (Answer must be r and h in terms of R where r & h are the radius and heighth of the cylinder). Have the answer, can't get it or find my error doing so!