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...
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...
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...