Calculus
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- Math
The mathematics of change. ðŸŒ
FAQ
Is dy/dx a function?
Limits
Basic idea: When \(x\) is approaching the some number, what is \(f(x)\)/\(y\)/the function approaching?
- For \(f(x)=\frac{x-1}{x-1}; f(x)=1, x\ne1\) i.e there is a discontinuity.
- \(\lim\limits_{x\to1}\frac{x-1}{x-1}=1\) means that \(f(x)\) is also approaching 1 as \(x\) is approaching 1.
Another example,
\(g(x)=\begin{cases} x^2,x\ne2\\ 1,x=2 \end{cases}\)
- \(\lim\limits_{x\to2}g(x)=4\) 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