Need help redoing two exam problems.

Hey everyone!

With finals approaching, I'm taking it upon myself to redo exam problems I didn't get full points on, starting with the following:

http://imageshack.us/a/img18/8130/60041868.jpg

As you can see, I've already attempted to redo that question on my own (in red) , but it worries me that I ended up with the same exact answer I had on the test.

Next...

http://imageshack.us/a/img132/1406/86285916.jpg

I did get the particle is at rest when t=0, which turned out to be correct, but I can't seem to figure out when else. Any ideas?

Re: Need help redoing two exam problems.

7.) We see that $\displaystyle f(2)=g(2)=0$ and so the limit is of the indeterminate form 0/0, so applying L'Hôpital's rule, we may state the limit as:

$\displaystyle \lim_{x\to2}\frac{f'(x)}{g'(x)}$

Now, use the slopes of the given tangent lines to complete the computation.

Your reworking looks good, you were probably penalized the first time for using the equations of the tangent lines in the limit.

9.) Differentiating with respect to $\displaystyle t$, we find the velocity function:

$\displaystyle v(t)=-\frac{\pi}{3}\sin\left(\frac{\pi}{3}t \right)$

The particle is at rest when $\displaystyle v(t)=0$.

$\displaystyle -\frac{\pi}{3}\sin\left(\frac{\pi}{3}t \right)=0$

$\displaystyle \sin\left(\frac{\pi}{3}t \right)=0$

This implies:

$\displaystyle \frac{\pi}{3}t=k\pi$ where $\displaystyle k\in\mathbb{Z}$

So let $\displaystyle t=3k$, and we must then have $\displaystyle k\in\{0,1\}$

Re: Need help redoing two exam problems.

Thank you! :)

So, for #9, I take it the particle is at rest when t equals 0 and 3, correct? (Worried)

Re: Need help redoing two exam problems.

Yes, that's right. Try substituting for t = 3 to verify the velocity function is zero there.

Re: Need help redoing two exam problems.

the particle is also at rest at t = 6, but apparently we stopped measuring just before it stopped moving (perhaps out of boredom.....). i've often wondered how one can do such a thing.

of course, perhaps something terrible happens at t = 6 (like, the particle died. i dunno).

Re: Need help redoing two exam problems.

Quote:

Originally Posted by

**MarkFL2** Yes, that's right. Try substituting for t = 3 to verify the velocity function is zero there.

I did, and I got zero. :)

Quote:

Originally Posted by

**Deveno** the particle is also at rest at t = 6, but apparently we stopped measuring just before it stopped moving (perhaps out of boredom.....). i've often wondered how one can do such a thing.

of course, perhaps something terrible happens at t = 6 (like, the particle died. i dunno).

Haha. Priceless. (Rofl)

Re: Need help redoing two exam problems.

Quick question. How do I mark this thread as SOLVED?

Re: Need help redoing two exam problems.

Try editing your first post, and look for a prefix text-box, which should have a drop-down menu to select the [SOLVED] option.

Re: Need help redoing two exam problems.

Quote:

Originally Posted by

**MarkFL2** Try editing your first post, and look for a prefix text-box, which should have a drop-down menu to select the [SOLVED] option.

I tried, but it wouldn't let me. For some reason, the 'Edit Post' option has disappeared...

Re: Need help redoing two exam problems.

I guess there is a time limit imposed on editing then...I know on the math forum I help to moderate, we have such a time limit imposed as an anti-spam measure.

Re: Need help redoing two exam problems.

Quote:

Originally Posted by

**MarkFL2** I guess there is a time limit imposed on editing then...I know on the math forum I help to moderate, we have such a time limit imposed as an anti-spam measure.

Makes sense... Thank you.