Calculus

tags : Math

The mathematics of change. 🌠

Limits §

Basic idea: When $x$ is approaching the some number, what is $f(x)$/$y$/the function approaching?

• For $f(x)=\frac{x-1}{x-1};f(x)=1,x\ne 1$ i.e there is a discontinuity.
• $\underset{x\to 1}{\lim }\frac{x-1}{x-1}=1$ means that $f(x)$ is also approaching 1 as $x$ is approaching 1.

Another example,

$g(x)=\{\begin{array}{l}{x}^2,x\ne 2\\ 1,x=2\end{array}$

• $\underset{x\to 2}{\lim }g(x)=4$ means that $g(x)$ is approaching 4 as $x$ is approaching 2.
• But we can see that as soon as $x$ is 2, $g(x)$ will be $1$.

Source: Introduction to limits - Khan Academy

Links §

• Limits & Continuity (1 of 3: Formal intro to limits)
• 3b1b
• Section 2-8 : Limits At Infinity, Part II