which of the statements a through i about the function ( y = f(x) ) graphed here are true, and which are…

which of the statements a through i about the function ( y = f(x) ) graphed here are true, and which are false?\na. the statement ( lim_{x\rightarrow2}f(x) ) does not exist is false.\nb. the statement ( lim_{x\rightarrow2}f(x)=2 ) is false.\nc. the statement ( lim_{x\rightarrow1}f(x) ) does not exist is true.\nd. the statement ( lim_{x\rightarrow c}f(x) ) exists at every point ( c ) in ( (-1,1) ) is

which of the statements a through i about the function ( y = f(x) ) graphed here are true, and which are false?\na. the statement ( lim_{x\rightarrow2}f(x) ) does not exist is false.\nb. the statement ( lim_{x\rightarrow2}f(x)=2 ) is false.\nc. the statement ( lim_{x\rightarrow1}f(x) ) does not exist is true.\nd. the statement ( lim_{x\rightarrow c}f(x) ) exists at every point ( c ) in ( (-1,1) ) is

Answer

Explanation:

Step1: Recall the definition of the limit

The limit of a function (y = f(x)) as (x\to c), (\lim_{x\to c}f(x)=L) if and only if (\lim_{x\to c^{-}}f(x)=\lim_{x\to c^{+}}f(x) = L)

Step2: Analyze the function for (x\in(-1,1))

For any (c\in(-1,1)), the left - hand limit (\lim_{x\to c^{-}}f(x)) and the right - hand limit (\lim_{x\to c^{+}}f(x)) are equal.

Answer:

True