What must be true for a limit to exist? In order to say the limit exists, the function has to approach the same value regardless of which direction x comes from (We have referred to this as direction independence). Since that isn't true for this function as x approaches 0, the limit does not exist.
Do all limits always exist?
This is the only section in which we will do this. Tables of values should always be your last choice in finding values of limits. The last two examples showed us that not all limits will in fact exist. We should not get locked into the idea that limits will always exist.
Why do limits fail to exist?
Quick Summary. Limits typically fail to exist for one of four reasons: The one-sided limits are not equal. The function doesn't approach a finite value (see Basic Definition of Limit). The function doesn't approach a particular value (oscillation). The $$x$$ - value is approaching the endpoint of a closed interval.
Should we get locked into the idea that limits always exist?
We should not get locked into the idea that limits will always exist. In most calculus courses we work with limits that almost always exist and so it’s easy to start thinking that limits always exist. Limits don’t always exist and so don’t get into the habit of assuming that they will.
Why do we do limits?
If we don’t do at least a couple of limits in this way we might not get all that good of an idea on just what limits are. The second reason for doing limits in this way is to point out their drawback so that we aren’t tempted to use them all the time! We will eventually talk about how we really do limits.
What must exist for a limit to exist?
If the function has both limits defined at a particular x value c and those values match, then the limit will exist and will be equal to the value of the one-sided limits. If the values of the one-sided limits do not match, then the two-sided limit will no exist.
What does existence of limit mean?
We know that for limit to exist at any value of x, say x=c exists only when limit approaching from right of c and limit approaching from left of c are equal. Condition for limit to exist at x=c. Assuming f(x) is piece-wise function.
Which of the following is not true about the existence of a limit function?
First is if one side, one of the sides of limit exists, then the limit yes does not exist. If one of the sides of the limited just then the limit of that function does not exist. Yeah, this is true, but both sides exist.
What are the three conditions for a limit to exist?
Definition. A function f(x) is continuous at a point a if and only if the following three conditions are satisfied: f(a) is defined limx→af(x) lim x → a f ( x ) exists. limx→af(x)=f(a)
Do function and limit take the same value?
It is important however, to not get excited about things when the function and the limit do not take the same value at a point.
Can graphs of functions be used to get limits?
So, while graphs of functions can, on occasion, make your life easier in guessing values of limits they are again probably not the best way to get values of limits. They are only going to be useful if you can get your hands on it and the value of the limit is a “nice” number.
Question 3
True or False. The graph of a rational function may cross its vertical asymptote.
Question 4
True or False. The graph of a function may cross its horizontal asymptote.
Question 6
True or False. If lim f (x) and lim g (x) exist as x approaches a then lim [ f (x) / g (x) ] = lim f (x) / lim g (x) as x approaches a.
Question 7
True or False. For any polynomial function p (x), lim p (x) as x approaches a is always equal to p (a).
Question 8
True or False. If lim f (x) = L1 as x approaches a from the left and lim f (x) = L2 as x approaches a from the right. lim f (x) as x approaches a exists only if L1 = L2.
Question 9
True or False. lim sin x as x approaches very large values (+infinity) is + 1 or - 1.
