Circle the two statements below that are true. For the remaining three false sta
ID: 2880325 • Letter: C
Question
Circle the two statements below that are true. For the remaining three false statements, sketch a graph of a function demonstrating that it is false. If lim_x rightarrow 0 f(x) = f (a) then f is continuous at x = alpha. If f is not continuous at x = a then f(a) notequalot lim_x rightarrow a f(x). If is not continuous at x = a then f(a) is undefined. If f is not continuous at x = a then lim_x rightarrow a f (x) does not exist. If f is not continuous at x = a then either f(a) is undefined or lim_x rightarrow a f (x) does not exist.Explanation / Answer
Statement a,b,d are right.
Wrong statements are c and e.
c) If f is not continuous at a, then f(a) is undefined.
This statement is false. Consider the following example
f(x) = x-3, if x not equals 0
= 2 if x =0
The above function is not continuous at x =0 but f(0) is well defined.
e) If f is not continuous at x=a, then either f(a) is not defined or limit x tends to a f(x) does not exist.
Consider the function f(x) = sin x/x, if x not equal to 0
= 2 if x equals 0
In this function limit x tends to 0 exists and equals 1.
f(0) is also well defined. But funciton is not continuous at x =0