So I just have basic questions about limits which I just need to clear up. So when I'm solving for a limit , when the greater exponent is on the top of the fraction ex: x^2+2x/x+1 then the limit will always =infinity? And how do u know when a limit = 0 ? I just don't want to be confused on my exam tomrow, please help explain :)

yes, the limit is always ∞.The limit is Zero when the greater power is in the bottom.

This is because when x gets really huge, on;y the highest power counts. You can throw all the lower degree stuff away.

So,

3x^3-7x+3
------------ -> 3x^3/x = 3x^2 -> ∞
x+4

If the powers are the same, then the limit is just the ratio of the coefficients:

3x^3-7x+3
--------------- -> 3x^3/6x^3 = 1/2
6x^3+9x^2-3x+2

More formally, you can divide top and bottom by the biggest power, and then since k/x -> 0 as x->∞, all the fractions with x in the bottom -> 0 and can be discarded.

3x^3-6x^2+4
----------------
6x^4-2x+7

Divide all by x^4 and you have

3/x - 6/x^2 + 4/x^4
-------------------------
6 - 2/x^3 + 7/x^4

now let x->∞ and you are left with

(3/x)/6 -> 0/6 = 0

So when the greater power is on top, the limit will equal infinity and when it's on the bottom then it will equal 0?

Yes, I believe that is what I said in my first sentence.

When solving for a limit, it is not always true that the limit will equal infinity just because the greater exponent is on the top of the fraction. It depends on the specific form of the limit.

In the case of the expression (x^2+2x)/(x+1), if you are evaluating the limit as x approaches infinity, then yes, the limit will be infinity. This is because as x gets larger and larger, the terms with lower exponents become negligible compared to the term with the highest exponent (x^2). As a result, the limit becomes dominated by the highest power of x, and the fraction grows without bound, approaching infinity.

However, if you are evaluating the limit as x approaches a certain finite value (say, 2), then the limit will not be infinity, because x is not becoming infinitely large. In this case, you would evaluate the limit by plugging in the value that x approaches and simplify the expression.

Regarding the limit equaling 0, it depends on the specific limit you are evaluating. Generally, a limit equals 0 if the numerator of the expression approaches 0 while the denominator becomes non-zero or finite. For example, consider the expression x/sqrt(x^2+1). As x approaches infinity, the numerator grows without bound, but the denominator also grows without bound because of the square root function. As a result, the limit will be 0.

On the other hand, if you have an expression like 1/x as x approaches infinity, in this case, the denominator (x) becomes infinitely large, while the numerator remains constant. In this scenario, the limit will be 0 since any non-zero constant divided by an infinitely large number approaches 0.

To determine the limit in a given scenario, it is essential to identify the form of the expression and consider the behavior of the numerator and denominator as x approaches the desired value.