Infinite Limits and Vertical Asymptotes
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Key Questions

Answer:
An infinite limit is what a functions y value approaches as it approaches infinity or negative infinity
Explanation:
An infinite limit is what a functions y value approaches as the x value approaches infinity or negative infinity
For example
#limxtooo e^x=oo#
#limxtooo e^x=0# 
The vertical asymptote is a place where the function is undefined and the limit of the function does not exist.
This is because as
#1# approaches the asymptote, even small shifts in the#x# value lead to arbitrarily large fluctuations in the value of the function.
On the graph of a function
#f(x)# , a vertical asymptote occurs at a point#P=(x_0,y_0)# if the limit of the function approaches#oo# or#oo# as#x>x_0# .For a more rigorous definition, James Stewart's Calculus,
#6^(th)# edition, gives us the following:"Definition: The line x=a is called a vertical asymptote of the curve
#y=f(x)# if at least one of the following statements is true:#lim_(x>a)f(x) = oo#
#lim_(x>a)f(x) = oo#
#lim_(x>a^+)f(x) = oo#
#lim_(x>a^+)f(x) = oo#
#lim_(x>a^)f(x) = oo#
#lim_(x>a^)f(x) = oo# "In the above definition, the superscript + denotes the righthand limit of
#f(x)# as#x>a# , and the superscript denotes the lefthand limit.Regarding other aspects of calculus, in general, one cannot differentiate a function at its vertical asymptote (even if the function may be differentiable over a smaller domain), nor can one integrate at this vertical asymptote, because the function is not continuous there.
As an example, consider the function
#f(x) = 1/x# .As we approach
#x=0# from the left or the right,#f(x)# becomes arbitrarily negative or arbitrarily positive respectively.In this case, two of our statements from the definition are true: specifically, the third and the sixth. Therefore, we say that:
#f(x) = 1/x# has a vertical asymptote at#x=0# .See image below.
Sources:
Stewart, James. Calculus.#6^(th)# ed. Belmont: Thomson Higher Education, 2008. Print. 
The vertical asymptote of
#y=1/(x+3)# will occur when the denominator is equal to 0. In this case, that will occur at 3, so the vertical asymptote occurs at#x=3# . There is no ycoordinate to be included.For a more thorough explanation behind vertical asymptotes, see here: http://socratic.org/questions/whatisaverticalasymptoteincalculus? In summary however, vertical asymptotes occur at
#x# values where the limit of the function, either overall or from the right or the left, approaches#+oo# .
Questions
Videos on topic View all (6)
Limits

1Introduction to Limits

2Determining One Sided Limits

3Determining When a Limit does not Exist

4Determining Limits Algebraically

5Infinite Limits and Vertical Asymptotes

6Limits at Infinity and Horizontal Asymptotes

7Definition of Continuity at a Point

8Classifying Topics of Discontinuity (removable vs. nonremovable)

9Determining Limits Graphically

10Formal Definition of a Limit at a Point

11Continuous Functions

12Intemediate Value Theorem

13Limits for The Squeeze Theorem