Math Help

[Giantzebra]

Does anyone know how to solve this problem? (attached)

[davewill]

Does anyone know how to solve this problem? (attached)

The answer is "e", infinity. As x approaches 2, f(x) approaches -1. That causes the denominator to approach 0, which causes the function as a whole to approach infinity.

[Giantzebra]

So because the denominator approaches zero the function approaches infinity?

[davewill]

So because the denominator approaches zero the function approaches infinity?

Yes. As the denominator gets smaller, the function as a whole keeps getting larger. 

1/1 = 1
1/0.01=100
1/0.00000000001 = 100000000000

It really doesn't matter what the numerator is so long as it's a real number.

[Giantzebra]

So because the denominator approaches zero the function approaches infinity?

Yes. As the denominator gets smaller, the function as a whole keeps getting larger. 

1/1 = 1
1/0.01=100
1/0.00000000001 = 100000000000

It really doesn't matter what the numerator is so long as it's a real number.

Does this mean that the answer would be infinity for any sine function?

[MrBossmanJr]

So because the denominator approaches zero the function approaches infinity?

Yes. As the denominator gets smaller, the function as a whole keeps getting larger. 

1/1 = 1
1/0.01=100
1/0.00000000001 = 100000000000

It really doesn't matter what the numerator is so long as it's a real number.

Does this mean that the answer would be infinity for any sine function?

Oh man, I haven't done this in awhile.

The graph shows that the limit as x approaches 2 should be -1, but it states that x / ( f(x) + 1) ). So, it would end up being 2 / ( -1 + 1 ) which is 2/0. 2 cannot be divided by 0 because it is not possible. Therefore, shouldn't the limit be undefined.

EDIT: Oh wait nevermind. You are suppose to fill in numbers close to that value to see where it would end up, hence being infinity.

I'm confused by the question "Does this mean that the answer would be infinity for any sine function?", but I think it would depend on what x is approaching for that particular expression.

[davewill]

Does this mean that the answer would be infinity for any sine function?

No. You have analyze the particular function and limit to figure out the answer. A different function or different limit would have different answer.

[Giantzebra]

How do you deal with this problem? (attached)

[mysonx3]

All I see in the document is a function. What is the question asking you to do?

[MrBossmanJr]

I'm guessing you are trying to find the derivative.