Need for limits

Limits help us understand the behavior of a function at points even when its not explicitly defined. \

Activity
Consider the function $$f(x)=e^{\frac{-1}{x^2}}$$

We want to know about the behavior of function at $$x=0$$however $$f(0)$$is not defined since $$\frac{1}{0}$$can't be operated upon. To solve this dilemma we will look at the behavior of $$f(x)$$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
We can see that as the values approach 0, $$f(x)$$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 $$f(x)$$starts getting bigger.

The same can be observed from the plot.