Q. 1 - Calculus

Question

Fill in the blanks to complete each of the following theorem statements: 

If $\underset{x\to c}{\lim }f\left(x\right)=L$and$\underset{x\to c}{\lim }f\left(x\right)=M$, then                  . 

Step-by-Step Solution

Answer

If $\underset{x\to c}{\lim }f\left(x\right)=L$and $\underset{x\to c}{\lim }f\left(x\right)=M$, then$\underline{L=M}.$

Step 1. Given information.

The given incomplete statement is folowing.

If $\underset{x\to c}{\lim }f\left(x\right)=L$and $\underset{x\to c}{\lim }f\left(x\right)=M$, then                  . 

Step 2. Explanation.

Uniqueness of Limits

The uniqueness of Limits states that if a limit $\underset{x\to c}{\lim }f\left(x\right)$exists then it can be equal to one and only one number and values of a function $f\left(x\right)$cannot approach two different values L and M as x approaches c.

So, If $\underset{x\to c}{\lim }f\left(x\right)=L$and$\underset{x\to c}{\lim }f\left(x\right)=M$, then$\underline{L=M}.$.