What is a Limit?
In mathematics, a **limit** is the value that a function or sequence "approaches" as the input or index approaches some value. It's about what happens to a function's output as you get infinitely close to a point, not necessarily what happens at the point itself.
For example, consider the function $f(x) = x+2$. As $x$ gets closer and closer to 3, the value of $f(x)$ gets closer and closer to 5. We can write this as:
$$ \lim_{x \to 3} (x+2) = 5 $$The concept becomes important when a function is undefined at a certain point, like in the example below, where the function has a "hole".
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Video: Visualizing Limits! 🤯
Watch this video to see how to approach a point from both the left and right sides on a graph to find a limit. 📈
Practice Problems
Find the value of the limits!
1) What is $\lim_{x \to 4} (2x-1)$?
2) What is $\lim_{x \to 2} (x^2+1)$?
3) What is $\lim_{x \to 0} \frac{x^2-x}{x}$?
4) What is $\lim_{x \to \infty} \frac{1}{x}$?
⚡ Limits Speed Quiz
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