Question

Evaluate
lim x−6/∣x−6∣
x→6 .
a) 0
b) 1
c) -1
d) Does not exist

Answer 1

To evaluate the limit lim x→6 (x-6)/|x-6|, we need to consider the limit as x approaches 6 from the left and the right side. When x approaches 6 from the left side,

So The Correct Option is; c)-1.

Step-by-step explanation:

To evaluate the limit limx→6 (x-6)/|x-6|, we need to consider the limit as x approaches 6 from the left and the right side.

When x approaches 6 from the left side, x-6 will be negative, and |x-6| will be positive. So, the expression (x-6)/|x-6| will be negative, and the limit will be -1.

When x approaches 6 from the right side, x-6 will be positive, and |x-6| will also be positive. So, the expression (x-6)/|x-6| will be positive, and the limit will be 1.

Since the limit from the left side (-1) is not the same as the limit from the right side (1), the limit does not exist.

x-6 will be negative, and |x-6| will be positive. So, the expression (x-6)/|x-6| will be negative, and the limit will be -1.

When x approaches 6 from the right side, x-6 will be positive, and |x-6| will also be positive. So, the expression (x-6)/|x-6| will be positive, and the limit will be 1. Since the limit from the left side (-1) is not the same as the limit from the right side (1), the limit does not exist.