Q. 4 - Calculus

Question

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

$\underset{x\to c}{\lim }A{x}^n=?.$

Step-by-Step Solution

Answer

The value is $A{c}^k.$

Step 1. Given Information.

The given limit function is $\underset{x\to c}{\lim }A{x}^n=?.$

Step 2. Value of the limit.

Power functions are continuous on their domains. In terms of limits,  $A$is real and $k$is rational, then for all values $x=c$at which $x^k$is defined , we have,

$\underset{x\to c}{\lim }A{x}^k=A{c}^k$