First Calculus Exam Tomorrow, Help with a few problems?

[adamp319]

Hello everyone,

First of all, thanks for even considering my thread! I appreciate any help you can give. I've got a few problems that are bothering me:

1. Use your calculator to solve the equation: cos(1/8x) = 4x ... I just never get the right answer... The solution: .24988 (Can't really show my work for this one, as I'm completely stuck and I know it's probably a very simple solution)

2. Use the Squeeze Theorem to find the limit: lim, as x approaches 0, xsin(x) ... I have a hard time with trig, due to not paying attention in trig class (yet somehow managing an A) ... My best guess is I need to review some trig. I understand the squeeze theorem for the most part, but I have a hard time applying it with trigonometry.

3. If a ball is thrown into the air with a velocity of 40ft/s, its height inf eet after t seconds is given by y = 40t - 16t². a) Find the average velocity for the time period beginning when t = 1 and lasting 0.04 seconds. I was able to figure this out and got 7.4, because once I broke down the equation I was left with lim, as h approaches 0, 40 - 32t - 16h ... The problem is the next question:

b) Find the instantaneous velocity when t = 1, using any appropriate method from class. My answer when using that broken down equation is -8, but the correct solution is just 8. I'm not sure where I'm going wrong?

My work for this problem is attached: http://www16.speedyshare.com/files/30211299/download/scan0001.pdf (most of the top half of the page is scratch)

Your browser should be able to view that .PDF without downloading it. I couldn't get a good quality image from my scanner uploaded to any other site (<name removed>, tinypic)

Thanks again for any assistance that you can provide!
Adam

 

[tkhunny]

1. Use your calculator to solve the equation: cos(1/8x) = 4x ... I just never get the right answer... The solution: .24988 (Can't really show my work for this one, as I'm completely stuck and I know it's probably a very simple solution)

Can't really help without a clue what you are doing. Did you check of Degrees/Radians?

2. Use the Squeeze Theorem to find the limit: lim, as x approaches 0, xsin(x) ... I have a hard time with trig, due to not paying attention in trig class (yet somehow managing an A) ... My best guess is I need to review some trig. I understand the squeeze theorem for the most part, but I have a hard time applying it with trigonometry.

Well, it may be too late. A common approximation for very small x is x = sin(x). Maybe that will lead to something.

3. If a ball is thrown into the air with a velocity of 40ft/s, its height inf eet after t seconds is given by y = 40t - 16t². a) Find the average velocity for the time period beginning when t = 1 and lasting 0.04 seconds. I was able to figure this out and got 7.4, because once I broke down the equation I was left with lim, as h approaches 0, 40 - 32t - 16h ... The problem is the next question:

How did you get that? Tough to tell what you did.

b) Find the instantaneous velocity when t = 1, using any appropriate method from class. My answer when using that broken down equation is -8, but the correct solution is just 8. I'm not sure where I'm going wrong?

What does "broken down" mean? Again, not a clue what you are doing.

Really, if you are struggling this much with ALL this material, you're kinda toast. Good luck unless you can learn to communicate a little better - and maybe pay better attention in class.

 

[adamp319]

As in I factored the equation down to a workable one? I provided you with a scan of my entire work? How am I not communicating well enough?

As for number 3, I used the formula lim, as h approaches 0, f(x) = f(x+h) - f(x)/h ... the normal formula for the tangent line?

So it would be 40(t+h) - 16(t+h)^2 - (40(t) - 16(t)^2)/h ... Once worked, it boils down to 40 - 32t - 16h ... And I was able to get the correct solution of 7.4 with this answer, when I plug 1 into t and .04 into h... I just don't get how to get the instant velocity... Actually... I just realized it as I was typing... I'm supposed to plug 0 into H, so it would be 40-32*1 = 8 ... which is the correct solution. So disregard 3.

I'm not struggling with all of the material, it's 3 (edit: now only 2) problems on a pretty lengthy review?

But thanks for your "attempt" at helping me, and as well as encouraging me to give up. I figured this forum was freemathhelp.com. I'll try to figure it out on my own.

 

[tkhunny]

It is common not to open attachments, even those that appear innocuous. This makes your attempts at communication laudable, but not useful.

Thank you for additional information. So, you really have not met the general derivative? Still working with the definition? That would have been important to know from the beginning.

I'm sure you mean [f(x) - f(x+h)]/h, but this absolutely is NOT f(x). See, there are a few unclear moments in your writings.

On #1, did you check the calculator settings? What sort of calculator are you using? Does it have a [SOLVE] feature? Have you tried graphing on the same set of coordinate axes and zooming to the graphical solution?

I'm not discouraging you. I'm just telling you the truth and doing my best to drag useful information out of you. Keep up your efforts and we'll get along just fine.

 

[mmm4444bot]

I have a hard time with trig, due to not paying attention in trig class

Do you intentionally not pay attention?

What is your situation?

:?