If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

AP®︎ Calculus BC (2017 edition)

Course: AP®︎ Calculus BC (2017 edition)>Unit 1

Lesson 2: Analyzing limits graphically

Estimating limit values from graphs

In this video, we learn to estimate limit values from graphs by observing the function's behavior as x approaches a value from both left and right sides. If the function approaches the same value from both sides, the limit exists. If it approaches different values or is unbounded, the limit doesn't exist.

Want to join the conversation?

• At , why can't we say that the limit is infinity?
• "In order for a limit to exist, the function has to approach a particular value. In the case shown above, the arrows on the function indicate that the the function becomes infinitely large. Since the function doesn't approach a particular value, the limit does not exist."
• Does there have to be a gap in the equation to find the limit? What's the purpose of this? Also, when we find this number, is the number itself called the equation's "limit"?
• No, there does not have to be a gap. They are just for you understand that even if there is a "gap", by which I mean the function at that particular value is undefined or defined as something else that does not match the kind of approaching behavior of the function, the limit is not affected. The 'number itself' will not be the equation's limit, as it only refers to the limit of the function as x approaches one certain point on it.
• Hello, how come on the second graph, the Lim of g(7) is 2? Wouldn't the dot make the limit become two values, therefore making it not exist? I'm confused. Thank you!
• At g(7), the limit would not have two values. This is because the filled in dot is where the line is. The unfilled dot is where the two lines converge, but it is not a point on the line. You can think of it like a jump graph.
• In the first graph, why does the limit as x approaches 2 not exist? Why can't we define limit as two values.. does that not mean that the function of the given parabola is wrong? Should they not be two different functions?
• We cannot define limit as two values. You'll learn about the derivatives and you'll know that it's impossible to have two values. You'll have to find the slope of the tangent line at the certain point of x. And if the left limit and the right limit is different, there will be two slopes which are not possible. The slope could be also defined as a velocity. You cannot have two velocities at the same time. It's hard to explain if you didn't learn derivatives.
Hope this helps! If you have any questions or need help, please ask! :)
• Why is it called limit ? i have no idea why they call it limit. it does not seem to relate what it means
• "Limit" simply relates to the fact that the distance between x and c is gradually "limited" to zero.
• What's the difference between a function and a limit?
• A function is a relation between a set of inputs and permissible outputs with the property that each input is related to exactly one output. A limit is the value that a function approaches as the input approaches a given value.
• At why doesn't the limit exist? I thought it would be +infinity
• Positive infinity is not an "existent" limit. It is undefined or nonexistent. Alternatively, you could say that the limit tends off to infinity.
• is it ok to call the limit of g as x approaching 1 as positive infinity?
• You might hear people refer to a limit as being positive/negative infinity, though technically, the limit would not exist.
• In the last example, I didn't quite get why the limit does not exist.