Homework SourseFor the function fx 2x3 0 3 The limit as x approaches 3 from
For the function
f(x)= 2x-3, 0<(or equal to) x
4, x = 3
x^2-6x+12 3 < x
use algebra to find each of the following limits:
limx approaches 3+ f(x)=
limx approaches 3- f(x)=
limx approaches 3 f(x)=
f(x)= 2x-3, 0<(or equal to) x
4, x = 3
x^2-6x+12 3 < x
use algebra to find each of the following limits:
limx approaches 3+ f(x)=
limx approaches 3- f(x)=
limx approaches 3 f(x)=
Solution
(1)
When x approaches 3 from the right, x > 3.
The limit as x approaches 3 from the right of f(x) =
The limit as x approaches 3 from the right of (x^2 - 6x + 12) =
3^2 - 6(3) + 12 =
3
(2)
When x approaches 3 from the left, x < 3.
The limit as x approaches 3 from the left of f(x) =
The limit as x approaches 3 from the left of (2x - 3) =
2(3) - 3 =
3
(3)
The left-hand limit equals the right-hand limit.
Therefore the limit as x approaches 3 of f(x) is 3.
