Question

What is limit in basic calculus?

Answer 1

Limit:

• The limit is a value of a function as the input of the function approaches or is closer to some number.
• It is used for defining continuity, integrals, and derivatives in calculus.
• General form: $\underset{x\to a}{\lim }f\left(x\right)=L$

Example: $\underset{x\to 2}{\lim }\frac{x-2}{x^2-4}$

$\underset{x\to 2}{\lim }\frac{x-2}{x^2-4}=\underset{x\to 2}{\lim }\frac{x-2}{\left(x-2\right)\left(x+2\right)}$ $\left[\because \left(a^2-b^2\right)=\left(a+b\right)\left(a-b\right)\right]$

$\Rightarrow$$\underset{x\to 2}{\lim }\frac{x-2}{x^2-4}=\underset{x\to 2}{\lim }\frac{1}{\left(x+2\right)}$

$\Rightarrow$$\underset{x\to 2}{\lim }\frac{x-2}{x^2-4}=\frac{1}{\left(2+2\right)}$

$\Rightarrow$$\underset{x\to 2}{\lim }\frac{x-2}{x^2-4}=\frac{1}{4}$