Question

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

Find$\underset{x\to 2^{+}}{\lim }f\left(x\right).$

Short answer

The answer is -4.

Step-by-step solution

Step. 1 Given

We are given with a graph and the in the limit x tends to 2 from right 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 Right hand limit at $x=2$so we start tracing the graph and we see that as x approaches 2 from right side the value of y decreases and goes up to -4.

Therefore,

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