Recent content by kylera

In other words, when I try to obtain a function, it has to be able to return any real number value for some value t? Hence, x = t would work?

Homework Statement Solve for the vector function that represents the curve of intersection in the following two surface: z = sqrt(x^2 + y^2) and z = 1 + y Homework Equations The Attempt at a Solution Through blind trial and error, I managed to get the book-specified answer of x =...

That's a very good way to associate with the term "projection". I wish the book could put it that succinctly. Much much thanks!

I'm re-visiting calculus again, and I've stumbled onto the concepts of scalar and vector projections in the vector chapter. While keeping in mind which equation to use for what projection is quite doable, I cannot seem to see the purpose of keeping scalar and vector projections in mind. Can...

I posted this in a different board, but I think this is a better place, so I'm reposting. I'm taking a materials science class (in Korea) but I'd like a decent English-language textbook to supplement the class-recommended material. The specific class name in English is "MECHANICAL BEHAVIOR...

Well, I'm sorry if the question sounded silly and amateurish, but the book I'm using didn't emphasize that aspect.

In words, the sum of a geometric sequence can be written out to say "the first term divided by (1 minus the common ratio)". Does the first term also apply when the series starts with some other number n other than 1 (like 2 or 3, etc)? In other words, the first term is when n = some other number...

ARGH! Totally forgot that! Thanks!

Homework Statement Re-write the following fraction into the sum of fractions: 1/[(n^3)+n] Homework Equations None that I can think of. . . The Attempt at a Solution I first changed [(n^3)+n] to n[(n^2)+1], so by the rules, the aformentioned fraction should equate to (A/n) +...

Alternating Series and P-series "convergence" I couldn't resist trying out a pun. Anyway, onto the question: Homework Statement Test the series for convergence/divergence: \sum^{\infty}_{n=1}\frac{-1^{n-1}}{\sqrt{n}} Homework Equations Alternating Series Test and possibly p-series...

I should follow your example, write up the solution neatly and scan it. Here's my take as follows: The series starts with n=0, which means the first value will be x^2 because anything to the zeroth power is 1. But hold on a second. The first term is x^2. You see an x^2 right there. That...

Is it mathematically possible for a series to be first declared "possibly not divergent" via the Test For Divergence, then to be declared divergent by applying the Integral Test? On that tangent, does that mean that the Test For Divergence will only render the conclusions "definitely...

\frac{d}{dx}e^x=e^x is true because the derivative of x is 1 (by power rule = derivative of x is 1 * x^(1-1)). If, in place of x, there was a function based on x (for example, 2x + 1), you would have e^(2x+1) multiplied by the derivative of the function, resulting in 2e^(2x+1) by the Chain Rule...

I get the impression that unlike solving derivatives and integrals, sequences and series do not have a lot of...should I say...find-the-equation-and-solve-your-way element -- sorry if that comes out wrong. Maybe it seems to be less "rote math" and because of this, I'm having a hard time trying...

Homework Statement Find the limit of the sequence { sqrt(2), sqrt(2sqrt(2)), sqrt(2sqrt(2sqrt(2))) ... } Homework Equations Limit Laws?The Attempt at a Solution I wrote out the first five values in the sequence and came to the conclusion that this sequence could be written out as A_{n} =...