Question

What are the limit properties?

Answer 1

Properties of the limit are as follows:

• Constant multiple rule: Limit of the product of a constant and $f\left(x\right)$ is product of constant and limit of $f\left(x\right)$
  $\underset{x\to h}{\lim }cf\left(x\right)=c\underset{x\to h}{\lim }f\left(x\right)$
• Sum rule: Limit of the sum of two functions is the sum of a limit of the first function and limit of the second function
  $\underset{x\to h}{\lim [}f\left(x\right)+g\left(x\right)]=\underset{x\to h}{\lim }f\left(x\right)+\underset{x\to h}{\lim }g\left(x\right)$
• Difference rule: Limit of difference of two functions is a difference of limit of the first function minus the limit of the second function $\underset{x\to h}{\lim [}f\left(x\right)-g\left(x\right)]=\underset{x\to h}{\lim }f\left(x\right)-\underset{x\to h}{\lim }g\left(x\right)$
• Product rule: Limit of the product of two functions is a product of limit of each function
  $\underset{x\to h}{\lim [}f\left(x\right).g\left(x\right)]=\underset{x\to h}{\lim }f\left(x\right).\underset{x\to h}{\lim }g\left(x\right)$
• Constant rule: Limit of a constant is constant itself
  $\underset{x\to h}{\lim }c=c$
• Quotient rule: Limit of the division of two functions is the division of limit of first function and limit of other function.
  $\underset{x\to h}{\lim }\frac{f\left(x\right)}{g\left(x\right)}=\frac{\underset{x\to h}{\lim }f\left(x\right)}{\underset{x\to h}{\lim }g\left(x\right)}$