Limits are super important for figuring out if a function is continuous or not! Here’s why:
Limits help us see what a function gets close to when we near a certain point.
For example, when we say “the limit as x approaches a of f(x) equals L,” it shows us what value f(x) is getting closer to as x gets near a.
A function is continuous at a point a if three things are true:
f(a) is defined.
The limit as x approaches a of f(x) exists.
The limit as x approaches a of f(x) is equal to f(a).
Using limits, we can find points where functions might “break” or jump.
This helps us understand if the function is smooth!
Limits are super important for figuring out if a function is continuous or not! Here’s why:
Limits help us see what a function gets close to when we near a certain point.
For example, when we say “the limit as x approaches a of f(x) equals L,” it shows us what value f(x) is getting closer to as x gets near a.
A function is continuous at a point a if three things are true:
f(a) is defined.
The limit as x approaches a of f(x) exists.
The limit as x approaches a of f(x) is equal to f(a).
Using limits, we can find points where functions might “break” or jump.
This helps us understand if the function is smooth!