Math Modeling - Limits

[ksu11grad]

Our teacher did not explain limits very well and he gave us a few example problems to work on, but I dont know where to start. The question looks like this:

Compute the following limits (if possible):
a)lim as x->infinity (-3+x^-1/4)

b)lim as X->0 (x^2-3x-1/3)

c)lim f(x) as x->1, where f(x)={0 if x is composed of Q), 1 if x is not composed of Q}

In A and B, I started to use a t-chart to show the values of x as it approached infinity, but wasn't sure if that was the correct way to show that.

C has me baffled. The way he wrote the test (yes, it's handwritten) he has the "Q" as a scripted Q, which to my understanding means "fractions/rationals".

 

[Deleted member 4993]

Our teacher did not explain limits very well and he gave us a few example problems to work on, but I dont know where to start. The question looks like this:

Compute the following limits (if possible):
a)lim as x->infinity (-3+x^-1/4)

You should know, 1/(infinity) = 0

b)lim as X->0 (x^2-3x-1/3) <-- something wrong with the problem statement

c)lim f(x) as x->1, where f(x)={0 if x is composed of Q), 1 if x is not composed of Q}

When x is not Q - then x is irrational. How many irrational points are there between two rational points? If don't know, do a Google search and let us know what you found.

In A and B, I started to use a t-chart to show the values of x as it approached infinity, but wasn't sure if that was the correct way to show that.

C has me baffled. The way he wrote the test (yes, it's handwritten) he has the "Q" as a scripted Q, which to my understanding means "fractions/rationals".

 

[ksu11grad]

Our teacher did not explain limits very well and he gave us a few example problems to work on, but I dont know where to start. The question looks like this:

Compute the following limits (if possible):
a)lim as x->infinity (-3+x^-1/4)

You should know, 1/(infinity) = 0

I dont understand, where would I divide 1 by infinity?

b)lim as X->0 (x^2-3x-1/3) <-- something wrong with the problem statement

As in there is something wrong with the way the question is worded?

c)lim f(x) as x->1, where f(x)={0 if x is composed of Q), 1 if x is not composed of Q}

When x is not Q - then x is irrational. How many irrational points are there between two rational points? If don't know, do a Google search and let us know what you found.

There are an infinite number of irrational points between 2 rationals.

In A and B, I started to use a t-chart to show the values of x as it approached infinity, but wasn't sure if that was the correct way to show that.

C has me baffled. The way he wrote the test (yes, it's handwritten) he has the "Q" as a scripted Q, which to my understanding means "fractions/rationals".

 

[Deleted member 4993]

Our teacher did not explain limits very well and he gave us a few example problems to work on, but I dont know where to start. The question looks like this:

Compute the following limits (if possible):
a)lim as x->infinity (-3+x^-1/4)

You should know, 1/(infinity) = 0

I dont understand, where would I divide 1 by infinity?

x^(-1/4) = (1/x)^(1/4)

b)lim as X->0 (x^2-3x-1/3) <-- something wrong with the problem statement

As in there is something wrong with the way the question is worded?

Is it

\(\displaystyle \frac{x^2 - 3x - 1}{3}\\)

or

\(\displaystyle x^2 - 3x - \frac{1}{3}\\)

or

something else?

If either of the first two - the limit is simply substitute 'x' by its limiting value. Where are you stuck?
c)lim f(x) as x->1, where f(x)={0 if x is composed of Q), 1 if x is not composed of Q}

When x is not Q - then x is irrational. How many irrational points are there between two rational points? If don't know, do a Google search and let us know what you found.

There are an infinite number of irrational points between 2 rationals.

Now think about the limit of the function as you trvel between two rational numbers.

In A and B, I started to use a t-chart to show the values of x as it approached infinity, but wasn't sure if that was the correct way to show that.

C has me baffled. The way he wrote the test (yes, it's handwritten) he has the "Q" as a scripted Q, which to my understanding means "fractions/rationals".

 

[ksu11grad]

A) I understand what you are saying now, not sure why didnt see that in the first place. So no matter what, the limit is going to be -3?

B) It is like the second one you listed. So doing the "t-chart", and assigning values for X is correct?

C) Did I answer my own question?