Help needed to evaluate limits

[Kendall]

Hello,

I am trying to do these problems, so far I only solve one correctly.
The graph of f(x) and g(x) are given in photos. I need to evaluate each quantity (please, see photo). I got right answer only for 3 one, which is 0.

Can someone help me to find the others?
Thank you!

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[stapel]

As you were asked elsewhere, which graph is which? What did you try for exercises (1), (2), and (4)? What were your answers?

Please be complete. Thank you!

 

[Kendall]

Hi, my post wasn't placed right away, only in 6 hours after I submitted, so when I realized that I didn't specified graph I couldn't edit it sooner, sorry. The red graph is f(x), and blue graph is g(x). As I said I only got answer for question (3) is 0.
I did question (1) , but not sure it is 1???
2) is 3??
4) is 3??

 

[stapel]

The red graph is f(x), and blue graph is g(x). As I said I only got answer for question (3) is 0.
I did question (1) , but not sure it is 1???
2) is 3??
4) is 3??

Since you do not provide your thoughts or steps, there is no way for us to comment on that. Also, the lack of a scale on the x-axes of the graphs is crippling. For instance, the limit of g(x) as x tends toward 1 is clearly y = 2, but where is x = 2 on the graph of f(x)? We cannot tell.

It might help if your instructor could provide more professional graphics for the homework assignment.

 

[Kendall]

Since you do not provide your thoughts or steps, there is no way for us to comment on that. Also, the lack of a scale on the x-axes of the graphs is crippling. For instance, the limit of g(x) as x tends toward 1 is clearly y = 2, but where is x = 2 on the graph of f(x)? We cannot tell.

It might help if your instructor could provide more professional graphics for the homework assignment.

Thanks for answering, yes there is no scale, but I guess we can approximate...
The steps I did are just trying to locate the parts of graphs and value of functions when x goes to certain place or value of functions are given.
I am sorry if I didn't explain it well. I will try again:
EX 1)I got my answer by looking at graph, for first question when x goes to 1- it looks like g(x) is 1 (blue graph).
EX 2) I also look where f(1) and g(1) are on the graph, so f(1)=1 + g(1)=0 therefore the answer is 1, but it is not correct answer.
EX 3) I just multiplied both functions, checking on the graph value of each when x goes to 1+. I got correct answer 0
EX 4) same thing here I look at both functions at x goes to 0+ and multiply them, so the answer I got is 3
That is all I did. I hope I explained it well enough. Thanks
If it is still not clear, I guess it is OK, I will ask my Professor when I see him next class.
Thank you

 

[Ishuda]

Reading your posts I believe you are changing the values for different exercises and may have
f(0) = 3 from EX 4)
f(1) = 1 from EX 2) but maybe = 0 from EX 3) if you used g(1)=1
g(0) = 1 from EX 4)
g(1) = 1 from EX 1) and maybe EX 3) but = 0 from EX 2) and maybe EX 3)

It would be better to actually first write down the values you need
f(0) = 3
f(1) = ?
g(0) = 1
g(1) = ?

Then use those values to do the exercises

 

[Kendall]

Reading your posts I believe you are changing the values for different exercises and may have
f(0) = 3 from EX 4)
f(1) = 1 from EX 2) but maybe = 0 from EX 3) if you used g(1)=1
g(0) = 1 from EX 4)
g(1) = 1 from EX 1) and maybe EX 3) but = 0 from EX 2) and maybe EX 3)

It would be better to actually first write down the values you need
f(0) = 3
f(1) = ?
g(0) = 1
g(1) = ?

Then use those values to do the exercises

Thank you! I will try to do it your way! I will post later,
Thanks again!

 

[Kendall]

Reading your posts I believe you are changing the values for different exercises and may have
f(0) = 3 from EX 4)
f(1) = 1 from EX 2) but maybe = 0 from EX 3) if you used g(1)=1
g(0) = 1 from EX 4)
g(1) = 1 from EX 1) and maybe EX 3) but = 0 from EX 2) and maybe EX 3)

It would be better to actually first write down the values you need
f(0) = 3
f(1) = ?
g(0) = 1
g(1) = ?

Then use those values to do the exercises

Hi again,

I am very confused about how you came up with g(0)=1...??
Also, I think
f(1)=1??
g(1)=0 because of solid dot??

Can you or someone explain how to do this exercise and what is the logic behind all this? Someone from my class already asked prof about this exercise, but he didn't explain and said it is too easy to even ask a question about. So here goes my plan to ask him before class out of window...
Thanks

 

[Ishuda]

Hi again,

I am very confused about how you came up with g(0)=1...??
Also, I think
f(1)=1??
g(1)=0 because of solid dot??

For g(0): If you look at what you wrote above for EX 4) you said the product of f(0) and g(0) was 3. I assumed you meant f(0) was 3 and g(0) would then have to be one.

For f(1): The 1.0 label on the graph means x is 1. The graph touches the x axis at x=1, so the value of f(1) is zero.

For g(1): The solid dot (and open dot) are just markers and don't stand for any value. If you look straight up from the solid dot you will see the graph touches the second dotted line. Thus the value of g(1) is 2.

Can you or someone explain how to do this exercise and what is the logic behind all this? Someone from my class already asked prof about this exercise, but he didn't explain and said it is too easy to even ask a question about. So here goes my plan to ask him before class out of window...
Thanks

OK. First look at the graph of f to get
f(0) = 3
f(1) = 0
f(2) = 1
Now the graph of g
g(0) = 1
g(1) = 2
Since the functions are continuous, the left and right hand limits are just the function value. So
1. f(g(1)) = f(2) = 1
2. f(1) + g(1) = 0 + 2 = 2
3. f(1) g(1) = 0 * 2 = 0
4. f(0) g(0) = 3 * 1 = 3

Of course this is my interpretation because we don't have any scales on the graphs as stapel pointed out. If someone else wanted to assign different numbers than that I would certainly expect their answers to be close to mine or else either have a pretty good explanation of how they got their values or point out where (they think) I made a mistake.

 

[Kendall]

Thank you, Ishuda!!!