# Finding the indicated limit?

limit of f of x as x approaches 5 where f of x equals 5 minus x when x is less than 5, 8 when x equals 5, and x plus 3 when x is greater than 5

0

8

3

The limit does not exist.

Relevance
• Hmm...🤔🤔... piecewise function.

f(x) = { 5 - x, x < 5

8, x = 5

x + 3, x > 5

Well, you already know what f(5) is -- 8. lim f(x) (x -> 5+) = 8. But lim f(x) (x -> 5-) = 0. You have a jump discontinuity at x = 5, so the overall limit does not exist.

• From the left, the limit approaches 5 - x --> 0

From the right, the limit approaches x + 3 --> 8

Since the values are different, the limit does not exist. It doesn't matter that exactly at x = 5, the value is 8; it only matters the behavior of the function from both sides as they approach 5. Since the values differ, there is no limit.

d) The limit does not exist.

• f(x) = 5-x : x < 5

= 8 : x = 5

= x+3 : x > 5

lim (x→ 5-) f(x) = 5-5 = 0

lim (x→ 5+) f(x) = 5+3 = 8

lim (x→5-) f(x) ≠ lim(x→5+) f(x) → lim(x→5) f(x) does not exist.

Ans: The limit does not exist.

• limit of f of x as x approaches 5 where f of x equals 5 minus x when x is less than 5, 8 when x equals 5, and x plus 3 when x is greater than 5

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