Limit Practice Problems

[nycmathdad]

See my answer to numbers 2, 4, 6, 8, and 10. Right or wrong?

Answers:

2. 3^5 = 243

4a. -1

4b. e

6a. (-3x) = (-3(2)) = -6

6b. (3x) = (3(0)) = 0

8. R(2)

10. When I cancel (x + 1) on the top and bottom, we can say that the limit of f(x) as x tends to -1 is the same as the limit of g(x) as x tends to -1.

 

[Steven G]

#8 is wrong.

 

[nycmathdad]

#8 is wrong.

What is the answer to 8?

 

[nycmathdad]

#8 is wrong.

I don't understand exactly what 8 is asking for.

 

[HallsofIvy]

We are told that R is a rational function and rational functions are continuous wherever they are defined. We are also told that R is defined for all x except x= 0. In particular, it is defined for x= 2 so is continuous there. \(\displaystyle \lim_{x\to 2} R(x)\) is indeed equal to R(2)! I don't know why Jomo said it is wrong.

 

[Dr.Peterson]

I don't understand exactly what 8 is asking for.

I believe that Jomo is pointing out merely that, although you are thinking correctly about #8, what you wrote is not what goes in the blank! There is already an R there ...

And the reason for saying it as he did is probably to make you think.

 

[nycmathdad]

We are told that R is a rational function and rational functions are continuous wherever they are defined. We are also told that R is defined for all x except x= 0. In particular, it is defined for x= 2 so is continuous there. \(\displaystyle \lim_{x\to 2} R(x)\) is indeed equal to R(2)! I don't know why Jomo said it is wrong.

Oh, so I am right. Wow! I don't know why Jomo said I am wrong.

 

[nycmathdad]

I believe that Jomo is pointing out merely that, although you are thinking correctly about #8, what you wrote is not what goes in the blank! There is already an R there ...

And the reason for saying it as he did is probably to make you think.

Dr. Peterson,

I am right. I found the answer online. R(2) is correct.

 

[jonah2.0]

Beer soaked ramblings follow.

... I found the answer online. R(2) is correct.

Hopefully, that will reduce your need to ask all these questions and your progress will go much faster; although the no pain no gain principle (as in almost every aspect of life) of studying does have its drawbacks. I guess you'll find out about it soon enough.