Answer :
Using the graph of g we get (a) value of function g at x=0 is 5
(b) [tex]\lim_{x \to \00} g(x)[/tex] or limit of g(x) at x=0 does not exist
(c) value of function g at x=1 is 4
(d) [tex]\lim_{x \to \11} g(x)[/tex] or limit of g(x) at x=1 is 4
What is limit of a function how can limit be interpreted using graph of that function?
Limit : Limit is the value that a function output approaches as the input approaches to a certain value.
For any function g(x) ,[tex]\lim_{x \to \22} g(x)[/tex] means that the value g(x) approaches as the x approaches to 2 .
From any graph we can easily see that to what value g(x)=y on the curve is approaching when the x is approaching to some value on x axis and if the graph is breaking on the value where x is approaching then the limit does not exist for that value of x.
For given graph
We can see value of value of function g at x=0 is 5 and value of function g at x=1 is 4
As the graph is breaking on x=0 into two functions then [tex]\lim_{x \to \00} g(x)[/tex] or limit of g(x) at x=0 does not exist
As the graph is not breaking at x=1 or we can say that graph of g(x)is approaching to 4 as x approaches to 1 then [tex]\lim_{x \to \11} g(x)[/tex] or limit of g(x) at x=1 is equal to g(1) that is 4
For more about limits,
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