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Evaluate the limits of g(x):

(i) Lim (x->3+) g(x)
(ii) Lim (x->3-) g(x)
(b) Does Lim (x->3) g(x) exist?

User MeloS
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1 Answer

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Final answer:

To evaluate the limits of g(x) as x approaches 3 from both directions, we consider the function's behavior near that point. The limit exists if the right-hand and left-hand limits are equal. Without an explicit function, exact limits cannot be computed but these principles guide the determination.

Step-by-step explanation:

To evaluate the limits of the function g(x) as x approaches 3 from the right (3+) and from the left (3-), without the explicit form of the function provided, we'll rely on the general knowledge of limits and continuity. Normally, we would look at the function's behavior near x = 3 and apply limit laws to determine Lim (x->3+) g(x) and Lim (x->3-) g(x).

Firstly, the right-hand limit (i) is found by observing the values that g(x) takes as x approaches 3 from values greater than 3. Similarly, the left-hand limit (ii) is determined by what happens to g(x) as x approaches 3 from numbers less than 3.

To answer part (b) about the existence of Lim (x->3) g(x), the limit exists only if the right-hand and left-hand limits are equal. If there is a discrepancy between them, the limit at x = 3 does not exist.

In summary, without an explicit function, we cannot compute the exact limits, but these are the concepts you would apply to determine them.

User Josep Bosch
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