Question

If limx→cf(x) exists, then limx→c1f(x) exists.
a) True
b) False

Answer 1

If the limit of a function as x approaches a constant c exists, then the limit of the same function multiplied by a constant 1 also exists.

Step-by-step explanation:

If the limit of a function f(x) as x approaches a constant c exists, it means that the function approaches a certain value as x gets arbitrarily close to c. In other words, the function has a well-defined output for values close to c. Now, if we multiply the function f(x) by a constant k (in this case, 1), it does not change the behavior of the function near c. Therefore, the limit of f(x) as x approaches c remains the same, and lim x→c (1)*(f(x)) = lim x→c f(x). Hence, the statement is True.