Question

Limit x tends to 3([x-3]+|x-4|)

Answer 1

Answer:

limx→3|x−3|x−3

Consider the left sided limit.

limx→3−|x−3|x−3

Make a table to show the behavior of the function |x−3|x−3

as x approaches 3

from the left.

x|x−3|x−32.9−12.99−12.999−1

As the x

values approach 3, the function values approach −1. Thus, the limit of |x−3|x−3 as x approaches 3 from the left is −1

.

−1

Consider the right sided limit.

limx→3+|x−3|x−3

Make a table to show the behavior of the function |x−3|x−3

as x approaches 3

from the right.

x|x−3|x−33.113.0113.0011

As the x

values approach 3, the function values approach 1. Thus, the limit of |x−3|x−3 as x approaches 3 from the right is 1

.

1

Since the left sided and right sided limits are not equal, the limit does not exist.

Does not exist