Q. 8 - Calculus

Question

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

$\underset{x\to c}{\lim }\sin x$= _

Step-by-Step Solution

Answer

The value is $c.$

Step 1. Given Information.

The given limit function is $\underset{x\to c}{\lim }\sin x$.

Step 2. Value of the limit.

The limit function can be written as,

$$\begin{gathered} =\underset{x\to c}{\lim }\sin x \\ =\underset{x\to c}{\lim }\sin x\times \frac{x}{x} \\ =\underset{x\to c}{\lim }\frac{\sin x}{x}\times x \{\frac{\sin x}{x}=1\} \\ =\underset{x\to c}{\lim }x \\ =c \end{gathered}$$