# Determining When a Limit does not Exist

Determining when a limit does not exist is a fundamental concept in calculus with practical applications in various fields such as physics, engineering, and economics. In mathematical terms, the limit of a function describes the behavior of the function as its input approaches a certain value. However, there are cases where this limit fails to exist, indicating significant behavior or discontinuity in the function. Identifying these scenarios is crucial for understanding the behavior of functions and their applications in real-world problems, making it an essential topic in calculus studies.

Questions

- For a given function #f(x)=x^a/x^b#, is it correct to say that #f(0)=0,1or"undefined"# depending on the values of #a# and #b#?
- How do you know a limit does not exist?
- Show that the function #|x|# is not differentiable at all points?
- What is an example of when a limit does not exist?
- How do you show the limit does not exist #lim_(x->4)(x-4)/(x^2-8x+16)# ?
- How do you show the limit does not exist #lim_(x->oo)sin(x)# ?
- How do you show the limit does not exist #lim_(x->6)(|x-6|)/(x-6)#
- How do you find the limit of #1/(x-1)# as x approaches 1?
- How does one prove this statement or provide a counterexample?
- What are some examples in which the limit does not exist?
- What is the limit as x approaches infinity of #sqrt(x)#?
- What is the limit of #(x^2 + x + 4)/(x^3 - 2x^2 + 7)# as x approaches a and when does the limit exist?
- What does limit does not exist mean?
- How do you use a graph to show that the limit does not exist?
- How do you prove that the limit #(3x + 5) = -1# as x approaches -1 using the formal definition of a limit?
- What is the limit as x approaches ∞ in the gamma function? Does it even exist?
- Evaluating Limits. Does the limit of #x ->-5# exist in the function #(x^3)/(x+5)^2#?
- How to evaluate #lim_(x->1) (x-2)/(x-1)# ?
- How do you find #\lim _ { x \rightarrow 0} \frac { - 2x ^ { 3} + x + 1} { x ^ { 2} + 3x }#?
- Lim ato0 (a+x)^3/a ?