Recent content by Greg

Looks good to me.

Here's the derivative for the function of power, $$ P=Av^2+\frac{B}{v} (\text{Where }A\text{ and }B\text{ are positive constants)} $$ that they give in the introduction to the problem: $$ P'(v)=2Av-\frac{B}{v^2} $$ To answer $$ \text{(a) What speed }vP\text{ minimizes power?} $$ we set this...

That depends on what a, b and c are.

yeah should have zoomed the page... lol... :)

In terms of getting useful replies, it would probably be best if you showed us where in the two problems you are having difficulty and how we can help. If you need to refer directly to the math in either of the two problems, please be quote it directly in your post. (clicking on the .pdf link...

\[ \lim_{N\rightarrow\infty}\frac{x}{2^n}\sin^2\left(\frac{x}{2^n}\right)\rightarrow0\times0^2\rightarrow0 \] but as the limit is taken over positive $x$ the limit tends to infinity.

There are a lot of online tutoring sites and which ones you may be interested in are are likely to be the ones concerning mathematics you want to study. https://khanacademy.org is one for elementary topics up to college/university topics.. https://desmos.com has a good online graphing calculator.

You need the roots $a,b$ of the equation $3\sqrt{x}-4=3x\sqrt{5}-\frac{8}{5}$ Once you have established these roots use them as endpoints in $\int_{a}^{b}\left(3\sqrt{x}-4-3x\sqrt{5}+\frac{8}{5}\right)dx$ The result is the area $A$ of $R$.

In general, periodic functions are of interest due to their frequent occurrence in natural phenomenon. As speculation, this particular function may be of interest due the times and places it occurs.

Note the concavity of $f(x)$. What does that tell you about lowering the graph of $f(x)$? (the line $y=0$ does not concern us presently).

Note the range of $f(x)$. A and B are vertical shifts, C and D are horizontal shifts. Which one of the given shifts would result in the graph of $f(x)$ not crossing the $x-\text{axis}$?

What do you get when you expand the LHS and equate the resulting terms with the corresponding terms in the RHS of the given equation

First, we need to establish $\sin\theta$ and $\cos\theta$. $9^2+(-5)^2=106$ (Pythagorean theorem) so $\sin\theta$ is $\sqrt{\frac{|-5|}{106}}, \text{that is}, \left(\frac{opp}{hyp}\right)$ and $\cos\theta$ is $\frac{3}{\sqrt{106}}, \text{that is}, \left(\frac{adj}{hyp}\right)$ (recall that...

Country Boy Is correct in stating that the slope of the tangent line is 2. So the tangent line equation is y = 2x + 3 and the equation of the normal is then y = -x/2 + 11/2

Haha!