Like what you saw?
Create FREE Account and:
- Watch all FREE content in 21 subjects(388 videos for 23 hours)
- FREE advice on how to get better grades at school from an expert
- Attend and watch FREE live webinar on useful topics
Limits: A Numerical Approach - ConceptFREE
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.
Stuck on a Math Problem?
Ask Genie for a step-by-step solution
Please enter your name.
Are you sure you want to delete this comment?
- One-Sided Limits 25,010 views
- Limits: A Graphical Approach 23,192 views
- Infinite Limits; Vertical Asymptotes 22,035 views
- Continuity 21,141 views
- Continuous Functions 19,972 views
- Evaluating Limits Algebraically, Part 1 16,772 views
- Evaluating Limits Algebraically, Part 2 15,154 views
- Limits and End Behavior 19,789 views