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If you know in advance that lim f(x) exists

x →4
you can determine the value of the limit by knowing all the values of f(x) for all x > 4?

A. True
B. False

User Cockypup
by
8.5k points

1 Answer

2 votes

Final answer:

The answer is B. False because to determine lim f(x) as x approaches 4, you need to consider the behavior of f(x) on both sides of x = 4, not just for x > 4.

Step-by-step explanation:

The correct answer is option B. False. Knowing the values of f(x) for all x > 4 does not allow you to determine the limit as x approaches 4. In order to find lim f(x) as x → 4, you need to know the behavior of f(x) on both sides of the point x = 4, meaning for values both greater than and less than 4. If f(x) is continuous at x = 4, then you can often infer the limit is equal to f(4). However, merely knowing the values for x > 4 is insufficient because the function could have a different behavior as x approaches 4 from the left, which could impact the actual limit value.

Knowing all the values of f(x) for all x > 4 does not allow us to determine the value of the limit lim f(x) as x approaches 4.Limit refers to the behavior of a function as x gets closer to a specific value, in this case, 4. To determine the value of the limit, we need to consider the behavior of the function f(x) as x approaches 4 from both sides, i.e., x → 4- and x → 4+. It is possible for the function to have different values or approaches on either side, making it necessary to consider the entire function and its behavior near x = 4 to accurately determine the limit.

User Juel
by
8.0k points
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