Question

Question 6 (4 marks) Is there a function f such that lim,+1 f(x) = 0 and lim→+1 Justify your answer.

Answer 1

There is no function f(x) that can fulfill function f such that lim,+1 f(x) = 0 and lim→+1

Step-by-step explanation:

For the given limit, lim x→+1 f(x) = 0, it means that as x approaches positive 1, the function f(x) approaches 0. However, if lim x→+1 g(x) ≠ 0, where g(x) represents the limit of another function as x approaches positive 1, then these two limits cannot be equal.

Therefore, no function f(x) can simultaneously satisfy lim x→+1 f(x) = 0 and lim x→+1 g(x) ≠ 0 for any other function g(x). This is because if the limit of f(x) is defined as 0 as x approaches positive 1, it cannot approach a different value other than 0 at the same limit point.

Hence, there is no function f(x) that can fulfill the given conditions.