### Learn math, science, English SAT & ACT from

high-quaility study
videos by expert teachers

##### Thank you for watching the video.

To unlock all 5,300 videos, start your free trial.

# Limits: A Numerical Approach - Concept

###### Norm Prokup

###### Norm Prokup

**Cornell University**

PhD. in Mathematics

Norm was 4th at the 2004 USA Weightlifting Nationals! He still trains and competes occasionally, despite his busy schedule.

In Calculus, the term limit is used to describe the value that a function approaches as the input of that function approaches a certain value. There are two ways to demonstrate **Calculus limits**: a numerical approach or a graphical approach. In the numerical approach, we determine the point where the function is undefined and create a table of values to determine the value of the variable as it approaches that point.

I want to talk about limits, limits are really important concept in Calculus, they're in everything in Calculus.

Let's start with the function f of x equals x cubed minus 125 over x-5, then you'll notice that this function is not defined of x=5 but we can still figure out what happens near x=5 and that's what limits are all about. So let's observe I've got I've made a table of values here and I have the inputs for 4, 4.9, 4.99, 4.999. These inputs are approaching five, what are the values doing? Well 61, 73.5 something 74.8 something, you can see that these outputs 9are getting closer and closer to it appears 75.

Now let's see what happens on the other side, so x is coming in towards 5 from the right now, 6, 5.1, 5.01 what's happening to the outputs. 91, 76.51, 75.15 75.015 you can see that here as well the values are getting closer to 75. So you can't plug 5 into this function but you can get as close as you want, and as you get closer and closer to 5 form both sides the value of the function is approaching 75. So here's what we say, we say that f of x approaches 75 as x approaches 5 or another way to write this and this is the way we will commonly express it the limit as x approaches 5 of f of x is 75.

Please enter your name.

Are you sure you want to delete this comment?

###### Norm Prokup

PhD. in Mathematics, University of Rhode Island

B.S. in Mechanical Engineering, Cornell University

He uses really creative examples for explaining tough concepts and illustrates them perfectly on the whiteboard. It's impossible to get lost during his lessons.

##### Concept (1)

#### Related Topics

- One-Sided Limits 26,626 views
- Limits: A Graphical Approach 25,409 views
- Infinite Limits; Vertical Asymptotes 24,810 views
- Continuity 23,283 views
- Continuous Functions 21,763 views
- Evaluating Limits Algebraically, Part 1 18,354 views
- Evaluating Limits Algebraically, Part 2 16,760 views
- Limits and End Behavior 22,985 views

## Comments (2)

Please Sign in or Sign up to add your comment.

## ·

Delete

## lerr · 6 months ago

how to prove lim h→0 ln x does not exist?

## nadine · 8 months, 1 week ago

Excellent demonstration. Clear, and to the point. Thank you .Very clear.