Q. 8 - Calculus

Question

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

Constant, identity, and linear functions are continuous everywhere, which means in terms of limits that        ,         , and           . 

Step-by-Step Solution

Answer

Constant, identity, and linear functions are continuous everywhere, which means in terms of limits that $\underline{\underset{x\to c}{\lim }k=k},\underline{\underset{x\to c}{\lim }x=c}$and$\underline{\underset{x\to c}{\lim }(mx+b)=mc+b.}$ 

Step 1. Given information.

The given incomplete statement is following. 

Constant, identity, and linear functions are continuous everywhere, which means in terms of limits that         ,           , and             . 

Step 2. Explanation.

Constant, identity and linear functions are continuous everywhere, which means in terms of limits that $\underline{\underset{x\to c}{\lim }k=k},\underline{\underset{x\to c}{\lim }x=c}$and $\underline{\underset{x\to c}{\lim }(mx+b)=mc+b.}$