What is the right-hand limit of this function at x=2?
g(x)=x^2−3/x−3
A) -1
B) 0
C) 1
D) 2
E) 3
well, plug in x=2 and see what you get.
Looks good to me.
When finding a limit, first try just plugging in the given value. As long as you don't wind up with 0/0 or something else undefined, the resulting value is the limit, as long as the function is not defined differently on the two sides.
To find the right-hand limit of a function at a specific point, we need to evaluate the function as the x-values approach the given point from the right side. In this case, we want to find the right-hand limit of the function g(x) as x approaches 2.
To do this, we substitute values that are slightly greater than 2 into the function and observe the pattern. Let's choose three values: x = 2.1, 2.01, and 2.001.
For x = 2.1:
g(2.1) = (2.1^2 - 3) / (2.1 - 3) = (4.41 - 3) / (-0.9) = 1.41 / -0.9 ≈ -1.567
For x = 2.01:
g(2.01) = (2.01^2 - 3) / (2.01 - 3) = (4.0401 - 3) / (-0.99) = 1.0401 / -0.99 ≈ -1.0516
For x = 2.001:
g(2.001) = (2.001^2 - 3) / (2.001 - 3) = (4.004001 - 3) / (-0.999) = 1.004001 / -0.999 ≈ -0.005
As we can see, as x approaches 2 from the right side, g(x) values seem to be approaching -1. Therefore, the right-hand limit of the function g(x) as x approaches 2 is -1.
Therefore, the correct answer is A) -1.