Q. 3 - Calculus

Question

Limits of basic functions: Fill in the blanks to complete the limit rules that follow. You may assume that k is positive 

$\underset{x\to c}{\lim }(mx+b)=?$

Step-by-Step Solution

Answer

The value is $m c+b.$

Step 1. Given Information.

The given limit function is $\underset{x\to c}{\lim }(mx+b).$

Step 2. Value of the limit.

We know,

For any linear function,

$$\begin{gathered} \underset{x\to c}{\lim }(mx+b)=\underset{x\to c}{\lim }mx+\underset{x\to c}{\lim }b \\ =\underset{x\to c}{m\lim }x+b \\ =mx+b \end{gathered}$$

Therefore,

$\underset{x\to c}{\lim }(mx+b)=mc+b$