The limit of function at x = 3 doest not exist and value of function will be f(3) = 5 so option (D) will be correct.
What is limit?
Limit, a nearness in mathematical notion, is largely used to give values to some functions at locations that were usually not given or defined, in a manner consistent with neighboring values.
In another word, limit is a mathematical concept in which we find out the value of any function at a point by its adjacent very close point.
Because the value of that function at that point doesn't define.
Given a function f(x)
As we can see that the function is breaking at x = 3 into two functions.
To exist any limit the left-hand limit must be equal to the right-hand limit
Left-hand limit
LHL = 3
Right-hand limit
RHL = 5
Since limits are not equal hence limits do not exist.
Now value of functon f(x) at x = 3 is 5 not 3 becuase at 3 the point is hollow while at x = 5 point is solid.
Hence,the limit of function at x = 3 doest not exist and value of function will be f(3) = 5
For more about limits,
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