Q. 34 - Calculus

Question

For each limit in Exercises 33–38, either use continuity to calculate the limit or explain why Theorem 1.16 does not apply.

$\underset{x\to -1}{\lim } x.$

Step-by-Step Solution

Answer

The limit exists and it is equal to -1.

Step 1. Given Information.

$$\begin{gathered} Given: \\ \underset{x\to -1}{\lim } x. \end{gathered}$$

Step 2. Theorem 1.16

$$\begin{gathered} Cons\tan t, identity, and linear functions are continuous everywhere. \\ In terms of limits, for every k, c, m, and b in R we have \\ \underset{x\to c}{\lim } k = k , \underset{x\to c}{\lim } x = c and \underset{x\to c}{\lim } (mx+b) = (mc+b). \end{gathered}$$

Step 3. Finding limit of given function.

$$\begin{gathered} U\sin g the above theorem\text{'}s 2nd case we have, \\ c = -1. \\ Putting this we get, \\ \underset{x\to -1}{\lim } x = -1. \end{gathered}$$