can anyone check if my answer is correct or not. The topic is about limits.
Advance thank you! :)

1. lim 8/(t-4)
t->4^+
my answer: positive infinity

2. lim (s-5)/(3s-2)
s->(2/3)^+
my answer: negative infinity

3. lim (1/t)-(1/t^2)
t->0^-
my answer: positive infinity

4. lim 2x/(x^2 - 2x)
x->2^-
my answer: positive infinity

5. lim (5-r)/((r-5)^2)
r->5^+
my answer: positive infinity

6. lim (x/x+2)+(1/x^2-4)
t-> -2^+
my answer: negative infinity


please correct my answer if it is wrong.

can anyone check if my answer is correct or not. The topic is about limits.
Advance thank you! :)


1. \lim_{t\to 4^{+}}\frac{8}{t-4}

my answer: positive infinity

Correct.


2. \lim_{s\to \frac{2^{+}}{3}}\frac{s-5}{3s-2}

my answer: negative infinity

Correct.


3. \lim_{t\to 0^{-}}\frac{1}{t}-\frac{1}{t^{2}}

my answer: positive infinity

should be {-\infty}


4. \lim_{x\to 2^{-}}\frac{2x}{x^{2} - 2x}

my answer: positive infinity

Should be {-\infty}


5. \lim_{r\to 5^{+}}\frac{5-r}{(r-5)^{2}}

my answer: positive infinity

Should be {-\infty}


6. \lim_{t\to -2^{+}}\frac{x}{x+2}+\frac{1}{x^{2}-4}

my answer: negative infinity

Correct. To help see why, look at their graphs.

Thank you! :)

I will assume that your notation :

lim
t -> 4^+

means the limit as t approaches 4 from the positive side. With this understanding - your first two answers are correct, but the last four are not. There are a couple of ways to check these:
1. You can graph the functions and see how they behave.
2. A quick check is to plug in a value for the variable that is very close to the limit, but offset a bit in the direction of interest. For example, in the third problem you have

lim (1/t)-(1/t^2)
t->0^-

So try plugging in t = -.01, and you get:
1/(-.01) - 1/(-.01)^2 = -100 - 10000 = -10100. It seems clear that this function is heading off to negative infinity as t approaches 0 from the negative side.

As for problem 6 - please clarify that what you meant is this:


\lim _ {t \to -2^+} (\frac x {x+2})+ (\frac 1 {x^2-4})

wait! In number 5. I just noticed.
I wrote r->5^+ and you wrote r->5^- .
Is the answer in number 5 is still negative infinity? :)

That was a typo on my part. It should be negative infinity if it is approaching 5 from the right.

Ok! Thanks a lot! :)

Is my answer in #6 correct or not?
I think my answer is wrong. :( it should be positive infinity?

Number 6 is negatve infinity.