I have a 3 part question and I'm not sure about my answers. Can you help? (It's for an online practice quiz)

1. http://i61.tinypic.com/2ugcw9c.jpg

2. http://i58.tinypic.com/346wak9.jpg w/ http://i59.tinypic.com/717bs7.jpg

3. http://i60.tinypic.com/mjsoi9.jpg

I'm pretty sure about part 1, but the other two I've spent a long time on and I keep getting different answers. What should I be getting?

Thanks!

For #1, you should have learned an arc length formula - you can just plug in the function and limits to get the answer.

- Hollywood

Originally Posted by hollywood
For #1, you should have learned an arc length formula - you can just plug in the function and limits to get the answer.

- Hollywood
For number one that's what I did. I thought I had that one right. Is it not? I was more worried about the other two parts.

I just started with #1. You've posted a lot of questions lately.

It's a lot easier to look at a solution and see if there's a problem as opposed to solving the problem and comparing results.

- Hollywood

Originally Posted by hollywood
I just started with #1. You've posted a lot of questions lately.

It's a lot easier to look at a solution and see if there's a problem as opposed to solving the problem and comparing results.

- Hollywood
I know I've posted a lot lately But thanks for helping me so much. It's from a ton of questions that my professor gave us that aren't for a grade but we're all struggling. I've asked other people in the class and they can't figure this one out. Did I get #1 right? Because I was pretty confident about it but now I'm not sure. And I don't even know where to start for the other two. I'm fairly certain I calculated #2 wrong.

Originally Posted by hollywood
I just started with #1. You've posted a lot of questions lately.

It's a lot easier to look at a solution and see if there's a problem as opposed to solving the problem and comparing results.

- Hollywood
I just tried to integrate each one over again for part 1. And the last option is about 8.5 when the one in the graph is 1.75. When I graph the options though the graph for the last option matches the graph in the question? Maybe I'm integrating them wrong but none of them ended up being 1.75, and the closest graph is the last one. Is the last one not right even though when I graph it out the graph looks really similar?

The formula for arc length is $L = \int_a^b \sqrt{1+(y')^2} \, dx$. Since $y = x^{-2}$, $y' = -2x^{-3}$, so the integrand is $\sqrt{1+(-2x^{-3})^2} = \sqrt{1+4x^{-6}}$, and the third answer is correct.

In #2, the fourth answer is correct. You bring $\Delta y$ out of the square root instead of $\Delta x$.

In #3, the second answer is correct.

- Hollywood

The formula for arc length is $L = \int_a^b \sqrt{1+(y')^2} \, dx$. Since $y = x^{-2}$, $y' = -2x^{-3}$, so the integrand is $\sqrt{1+(-2x^{-3})^2} = \sqrt{1+4x^{-6}}$, and the third answer is correct.
In #2, the fourth answer is correct. You bring $\Delta y$ out of the square root instead of $\Delta x$.