Question

Find lim f(x) where f(x) = { ( 7 - x, x < 4)(2, x=4)(pi/2+1, x > 4) x→4

Answer 1

To find the limit of f(x) as x approaches 4, we evaluate each case separately: x < 4, x = 4, and x > 4. The limit is 3 when x < 4, 2 when x = 4, and pi/2 + 1 when x > 4.

Step-by-step explanation:

The given function f(x) is defined as:

f(x) = { (7 - x, x < 4)(2, x=4)(pi/2+1, x > 4)

To find the limit of f(x) as x approaches 4, we need to consider the three cases:

1. x < 4: In this case, f(x) = 7 - x
2. x = 4: In this case, f(x) = 2
3. x > 4: In this case, f(x) = pi/2 + 1

To find the limit, we need to evaluate each case:

For x < 4:

lim f(x) = lim (7 - x) = 7 - 4 = 3

For x = 4:

lim f(x) = lim 2 = 2

For x > 4:

lim f(x) = lim (pi/2 + 1) = pi/2 + 1

Therefore, the limit of f(x) as x approaches 4 is 3 when x < 4, 2 when x = 4, and pi/2 + 1 when x > 4.