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vesna_86 [32]
3 years ago
14

Find the indicated limit, if it exists. limit of f of x as x approaches negative 1 where f of x equals 4 minus x when x is less

than negative 1, 5 when x equals negative 1, and x plus 6 when x is greater than negative 1 6 0 5 The limit does not exist.
Mathematics
1 answer:
UkoKoshka [18]3 years ago
7 0

Answer:

The limit is 5

Step-by-step explanation:

A limit exists if the one-sided limits are equal. So we analyze the limit by approaching it from both the left and the right.

From the left: \lim_{x \to \--1} F(x) =  \lim_{x \to \--1} (4-x) = 4-(-1) = 5

From the right: \lim_{x \to \--1} F(x) =  \lim_{x \to \--1} (x+6) = -1+6 = 5

At x= -1 itself: F(x) = 5

Since the limits when approaching from the left and right match, the limit does exist. Thus we conclude that the limit of f of x as x approaches negative 1 is five.

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