When we talk about limits in calculus, there are two types we often see: finite limits and infinite limits.
Finite Limits:
These happen when a function gets closer and closer to a specific number as it nears a certain point.
For example, let's look at the function ( f(x) = 3x + 1 ).
As ( x ) gets closer to 2, we calculate the limit:
( f(2) = 3(2) + 1 = 7 ).
So, we can write this as:
[ \lim_{x \to 2} f(x) = 7 ]
Infinite Limits:
These limits occur when the values of the function keep growing bigger or smaller without stopping, as ( x ) gets close to a certain value.
Take the function ( g(x) = \frac{1}{x} ).
As ( x ) approaches 0 from the right side, ( g(x) ) increases towards infinity:
[ \lim_{x \to 0^+} g(x) = \infty ]
To sum it up, finite limits give us a specific number, while infinite limits show us that the values are growing or shrinking without end.
Understanding these ideas helps us get a better grasp of how functions behave!
When we talk about limits in calculus, there are two types we often see: finite limits and infinite limits.
Finite Limits:
These happen when a function gets closer and closer to a specific number as it nears a certain point.
For example, let's look at the function ( f(x) = 3x + 1 ).
As ( x ) gets closer to 2, we calculate the limit:
( f(2) = 3(2) + 1 = 7 ).
So, we can write this as:
[ \lim_{x \to 2} f(x) = 7 ]
Infinite Limits:
These limits occur when the values of the function keep growing bigger or smaller without stopping, as ( x ) gets close to a certain value.
Take the function ( g(x) = \frac{1}{x} ).
As ( x ) approaches 0 from the right side, ( g(x) ) increases towards infinity:
[ \lim_{x \to 0^+} g(x) = \infty ]
To sum it up, finite limits give us a specific number, while infinite limits show us that the values are growing or shrinking without end.
Understanding these ideas helps us get a better grasp of how functions behave!