Question

In Problems 13–32, use the accompanying graph of y = f(x).

Find$\underset{x\to -4^{-}}{\lim }f\left(x\right).$

Short answer

The answer is 2.

Step-by-step solution

Step. 1 Given 

We are given with a graph and the in the limit x tends to -4 from left side.

Step. 2 Solving the limits

When we have the graph and we want to calculate the limit then we have to trace the graph from that direction whose side limit we want to find i.e., if we have to find Left hand limit then we start tracing the graph from left side and similarly if we have to find Right hand limit then we start tracing the graph from right side at that point at which we have to find the limit.

In this question we are required to find Left hand limit at $x=-4$so we start tracing the graph and we see that as x approaches -6 from left side the value of y increases and goes to $y=2$.

Therefore,

$\underset{x\to -4^{-}}{\lim }f\left(x\right)=2.$