Chapter 12.1, Problem 24E

To determine

The graph of the function and find the limit (if it exists) as x approaches 2.

Answer to Problem 24E

Limit of $f(x)$ as x approaches 2 does not exist.

Explanation of Solution

Given info:

  $f(x)=\{\begin{array}{l}-2x,x\le 2\\ x^2-4x+1,x>2\end{array}$

Formula used:

If f(x) becomes arbitrarily close to a unique number L as approaches c fromeither side, then the limit of f(x) as approaches c is L. This is written as

  $\underset{x\to c}{\lim }f(x)=L$

Calculation:

We need to plot the graph,

  

As the limit closes to 2 from left side the value of f(x) is -4 and as from the right the value is 3.

So limit does not exist.

Limit of $f(x)$ as x approaches 2does not exist.

Conclusion:

Thus,thelimit of $f(x)$ as x approaches 2 does not exist.