what happens as x approaches zero from the positive direction? what happens as x approaches zero from the…

Explanation:

Step1: Analyze right - hand limit

As (x) approaches (0) from the positive direction, we look at the values of (x = 0.001,0.01,0.1). The corresponding function values are (e,f,g). We need to observe the trend of these values. If the values seem to be getting closer to a certain number (L), then (\lim_{x\rightarrow0^{+}}f(x)=L). Without knowing the actual function, we can only say that we are looking at the sequence of values (e,f,g) as (x) gets closer to (0) from the positive side.

Step2: Analyze left - hand limit

As (x) approaches (0) from the negative direction, we look at the values of (x=- 0.001,-0.01,-0.1). The corresponding function values are (d,c,b). We observe the trend of these values. If they are getting closer to a number (M), then (\lim_{x\rightarrow0^{-}}f(x)=M).

Answer:

As (x) approaches zero from the positive direction, the function value approaches the value that the sequence (e,f,g) is converging to. As (x) approaches zero from the negative direction, the function value approaches the value that the sequence (d,c,b) is converging to.