help with limits question that i can't do in calculator

[nancyy]

i just started to learn about limits in the khan academy site, and in one quize i were given the following question

i tried to solve for x=4.0001 but i don't know what to do and i am confused with the brackets in the superscript, its an exponent? cause if so it didn't gave the result mentioned in the question for me, i got some 0.0000003
(or something like that) instead.

can somebody please explaine me what is going on?.
and another smaller question, do i need to learn about integrals before i learn about limits? cause in one of the questions about limits there was something with integral(In) in the question.

 

[ksdhart2]

I believe the attachment in question says the following:

Consider the table with function values f(x)=3(x-4)^(x-4) at positive x-values near 4. Notice that there is one value missing in the table.

Use a calculator to evaluate f(x) at x=4.0001 and enter this number in the table, rounded to the nearest 0.0000001

From the table, what does the one-sided limit:

\(\displaystyle \displaystyle \lim _{x\to 4}\left(3\left(x-4\right)^{\left(x-4\right)}\right)\)

appear to be?

Now, you say as part of your work:

i tried to solve for x=4.0001 but i don't know what to do and i am confused with the brackets in the superscript, its an exponent? cause if so it didn't gave the result mentioned in the question for me, i got some 0.0000003 (or something like that) instead. can somebody please explaine me what is going on?.

Yes, the superscript is an exponent, the same as you're used to seeing. To evaluate the expression f(4.0001), simply follow PEMDAS (or you may have learned it as BODMAS):

Parentheses (or Brackets)
Exponent (or Orders)
Multiplication/Division
Addition/Subtraction

You have an exponent, so that would seen to come first. But, oh, there's parentheses in that exponent, so you need to deal with that first. Since the exponent is (x-4), what does that equal when x=4.0001? Then proceed to evaluate the exponent. Finally, multiply by 3. The answer you got of 0.0000003 is very clearly the wrong answer

and another smaller question, do i need to learn about integrals before i learn about limits? cause in one of the questions about limits there was something with integral(In) in the question.

No, you don't need to know integrals to evaluate limits. It's actually the other way around - you can't study integrals without understanding limits. I can't speak to what the problem may or may not have meant by "In", but it certainly wasn't integral. That is always denoted by this symbol: \(\displaystyle \displaystyle \int\)