To determine the infinite limit as x approaches −5 from the right, we need to analyze the behavior of the function x+5x+6 as x gets closer to −5 from values greater than −5. Specifically, we should look at the numerator and the denominator separately to understand how the function behaves near this point.
Step 1: Define the Function and the Limit
We are given the function:
f(x)=x+5x+6
We need to find the limit as x approaches −5 from the right:
x→−5+limx+5x+6
Step 2: Analyze the Behavior of the Function Near x=−5
As x approaches −5 from the right (x→−5+):
The numerator x+6 approaches −5+6=1.
The denominator x+5 approaches −5+5=0 from the positive side.
Step 3: Determine the Sign of the Limit
Since the numerator approaches a positive value (1) and the denominator approaches zero from the positive side, the fraction x+5x+6 will grow without bound in the positive direction.