Difference between revisions of "Need for limits"
Jump to navigation
Jump to search
(Created page with "Limits help us understand the behavior of a function at points even when its not explicitly defined. \ === Activity === '''Consider the function <math>f(x)=e^{\frac{-1}{x^2}...") |
|||
| Line 6: | Line 6: | ||
We want to know about the behavior of function at <math>x=0</math>however <math>f(0)</math>is not defined since <math>\frac{1}{0}</math>can't be operated upon. To solve this dilemma we will look at the behavior of <math>f(x)</math>when x is near to 0. | We want to know about the behavior of function at <math>x=0</math>however <math>f(0)</math>is not defined since <math>\frac{1}{0}</math>can't be operated upon. To solve this dilemma we will look at the behavior of <math>f(x)</math>when x is near to 0. | ||
| − | '''In a spreadsheet, plot the values of f(x) as x is the 'neighborhood' of 0. Then plot the function and mark your observations.''' | + | '''In a spreadsheet, plot the values of f(x) as x is the 'neighborhood' of 0. Then plot the function and mark your observations.''' |
| + | |||
| + | === Solution === | ||
| + | {{Geogebra|frydyff2}} | ||
| + | We can see that as the values approach 0, <math>f(x)</math>get really really small and really close to 0 however at no point, does it touch 0. And as the values go away from 0 <math>f(x)</math>starts getting bigger. | ||
| + | {{Geogebra|bqh7e9dj}} | ||
| + | The same can be observed from the plot. | ||
Latest revision as of 12:10, 17 June 2022
Limits help us understand the behavior of a function at points even when its not explicitly defined. \
Activity
Consider the function
We want to know about the behavior of function at however is not defined since can't be operated upon. To solve this dilemma we will look at the behavior of when x is near to 0.
In a spreadsheet, plot the values of f(x) as x is the 'neighborhood' of 0. Then plot the function and mark your observations.
Solution
Download this geogebra file from this link.
We can see that as the values approach 0, get really really small and really close to 0 however at no point, does it touch 0. And as the values go away from 0 starts getting bigger.
Download this geogebra file from this link.
The same can be observed from the plot.