Any insight into sec. 2.1 #8? I found the derivative for part b, i think it's right but i'm not getting the answer im looking for. and i think i messed up part a. Any help?
For a), find the average velocity over each interval. For the interval [1,2] the average velocity is
[s(2) - s(1)]/(2-1).
Similarly for the rest.
For b), no need for the derivative. Just "guesstimate" from a). In a) the intervals are getting shorter, with the end point approaching 1. So in a) the average is estimating the derivative with greater accuracy as the intervals get shorter. To check how close you are, you could find the true derivative and plug in 1. (We haven't gotten to this yet, so the estimate is good enough.)
I figured out part a)(i). I got 6. I checked in the main website where it gives various even answers for the practice problems and it gave -4.71 or something along those lines, but by following the same guidelines as a)(i) i got around 60. So I'm not sure if for some reason I'm doing (ii) wrong, or the answer is just wrong on the website. Anything would help! thanks!
You're right. The answer for #8.a.i) is 6. For (ii) I also came up with -4.71. I suspect you have a simple sign error. (Did you accidentally add the numbers in the numerator?)
The example at the bottom of pg. 85 is very similar. The hint is that for 5.a.i), your start time is 2 and end time is 2.5, so the interval is [2, 2.5]. Then use the average velocity formula (see second post above or pg. 85 of Stewart). -Jesse
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6 comments:
Any insight into sec. 2.1 #8? I found the derivative for part b, i think it's right but i'm not getting the answer im looking for. and i think i messed up part a. Any help?
For a), find the average velocity over each interval. For the interval [1,2] the average velocity is
[s(2) - s(1)]/(2-1).
Similarly for the rest.
For b), no need for the derivative. Just "guesstimate" from a). In a) the intervals are getting shorter, with the end point approaching 1. So in a) the average is estimating the derivative with greater accuracy as the intervals get shorter. To check how close you are, you could find the true derivative and plug in 1. (We haven't gotten to this yet, so the estimate is good enough.)
I figured out part a)(i). I got 6. I checked in the main website where it gives various even answers for the practice problems and it gave -4.71 or something along those lines, but by following the same guidelines as a)(i) i got around 60. So I'm not sure if for some reason I'm doing (ii) wrong, or the answer is just wrong on the website. Anything would help! thanks!
You're right. The answer for #8.a.i) is 6. For (ii) I also came up with -4.71. I suspect you have a simple sign error. (Did you accidentally add the numbers in the numerator?)
On #5 I am not sure how to start it. I am can't quite get the equation/function set up, but I know the steps after that. any help?
The example at the bottom of pg. 85 is very similar. The hint is that for 5.a.i), your start time is 2 and end time is 2.5, so the interval is [2, 2.5]. Then use the average velocity formula (see second post above or pg. 85 of Stewart).
-Jesse
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