This topic is set up for Calc I folks to add questions and comments to our review sheet for quiz 1. All Calc I students should feel free to ask clear and specific questions about that review sheet. Better yet, students can post answers!
Also, please take a look at this post on how to format your posts well.
For the first question, would the answer be 7.388 or 7.4?
The amount of digits that repeat are consistent between the last few answers, but I assume that it implies the limit would reach 7.4.
Thoughts?
That’s a good question - thanks for asking!
Generally, the idea here is to look for stability in the digits, so I’d certainly accept 7.388 on the quiz. With that 7.38898 at the end, it’s awfully close to flipping the 8 in the thousands place. I don’t see any reason to think that it’s going to make it up to 7.4, though.
Of course, you’ve got the formula so, though you wouldn’t do this on the quiz, you can generate some more terms in the sequence. Doing so, I got this:
| x | 0.1 | 0.01 | 0.001 | 0.0001 | 0.00001 | 0.000001 | 0.0000001 |
|---|---|---|---|---|---|---|---|
| f(x) | 6.7275 | 7.31602 | 7.38168 | 7.38832 | 7.38898 | 7.38905 | 7.38906 |
So it looks like 7.38905 is probably a safe bet.
To be clear, though, on the quiz, I would have to accept 7.388 or 7.389, which are both within 0.001 of the actual answer.
I am kinda confused about the answer format or what answer you’re looking for in question 3a.
This question is all about “how do you read a graph”? This largely boils down to knowing the conventions that folks use when they draw and talk about graphs.
Let’s look at a similar picture, for example:
For that picture, I would say that f(3) = 2. The value of 2 is indicated by the filled dot that you see near the top right of the picture.
I would also say by contrast that the limit as x->3 is 1. That’s where the open dot is at the point (3,1).
I hope that makes sense!
Would 2B, just be me showing my work of how I got 1/2 as my answer?
For question 3 c and d how do I find a=4?
May I have an example of what a correct sentence for a #6 type of question would look like?
I don’t think that’s how I’d put it, no.
In number 2, you’re asked to think about a limit in a couple of different ways - graphically and analytically.
In part (a), you’re just asked to make a judgement on the value of the limit based on the graph. It’s pretty easy to see that the answer ought to be 1/2. There’s not much analytic work that goes into that at all.
In part (b), you’re asked to go through an analytic process to prove that the limit is, indeed, 1/2. The answer is the same but the process is different and those processes have different levels of reliability.
I don’t think the limit exists from that side because the function values aren’t defined to the right of a=4. Thus, the answer should be DNE.
You can find an example in this Colab notebook from Wednesday’s class.
It’s the Proof following the Claim in the section named “Example”.