Recent content by reinloch

Homework Statement Suppose we walk along a unit semicircle. Homework Equations Find the average value of our distance from the base of the semicircle. The Attempt at a Solution y_{ave} = \frac{1}{1-(-1)}\int_{-1}^1\sqrt{1-x^2}\ dx = \frac{\pi}{4} OR y = \sin\theta, \qquad 0...

This always bugs me, because assuming k > 0, as n → ∞, k/n → 0 from the right.

Hi all, regarding the proof of the general power rule, If we let y = x^r, then \ln y = r\ln x, and then by implicit differentiation \frac{y'}{y} = \frac{r}{x}, and thus it follows that y' = \frac{ry}{x} = \frac{rx^r}{r} = rx^{r-1}. But the statement \ln y = r\ln x also requires x>0, so...

Thanks. I am stuck with the right choice for \delta. I choose 1 and -\frac{1}{N}, and it didn't seem to work.

Homework Statement proof this limit: \lim_{x\rightarrow 1^+}\frac{1}{(x-1)(x-2)}=-∞ Homework Equations The Attempt at a Solution So for every N < 0, I need to find a \delta > 0 such that 0 < x - 1 < \delta \Rightarrow \frac{1}{(x-1)(x-2)} < N Assuming 0 < x - 1 < 1, I get...