Q. 21 - Calculus

Question

Limits of combinations: Fill in the blanks to complete the limit

rules that follow. You may assume that k and c are any real

numbers and that both $\underset{x\to c}{\lim }f\left(x\right) \mathrm{and} \underset{\mathrm{x}\to \mathrm{c}}{\lim }g\left(\mathrm{x}\right)$exist.

$\underset{x\to c}{\lim k}f\left(x\right) =\_\_\_\_\_\_\_$

Step-by-Step Solution

Answer

The value of the limit is $\underset{x\to c}{\lim k}f\left(x\right)=k\underset{x\to c}{\lim }f\left(x\right).$

Step 1. Given Information.

The given limit function is $\underset{x\to c}{\lim k}f\left(x\right).$

Step 2. Filling the blank.

To fill the blank, use the Constant Multiple Rule of limits.

So,

$\underset{x\to c}{\lim k}f\left(x\right)=k\underset{x\to c}{\lim }f\left(x\right).$