Q. 10 - Calculus

Question

Fill in the blanks to complete each of the following theorem statements: 

All algebraic functions are continuous on their domains, which means in terms of limits that if $x=c$is in the domain of an algebraic function f, then            . 

Step-by-Step Solution

Answer

 All algebraic functions are          on their domains, which means in terms of limits that if $x=c$is in the domain of an algebraic function f, then we can calculate $\underline{\underset{x\to c}{\lim }f\left(x\right)}$by evaluating $\underline{f\left(c\right)}.$

 

Step 1. Given information.

The given incomplete statement is the following. 

All algebraic functions are          on their domains, which means in terms of limits that if $x=c$is in the domain of an algebraic function f, then             . 

Step 2. Explanation.

All algebraic functions are continuous on their domains, which means in terms of limits that if x = c is in the domain of an algebraic function f, then 

we can calculate $\underline{\underset{x\to c}{\lim }f\left(x\right)}$ by evaluating $\underline{f\left(c\right)}.$