Let a=8, f(x)=|x-8|/x

Is the value of the limit 0.

To determine the value of the limit of the function f(x) as x approaches a certain value, we can use the concept of one-sided limits.

In this case, the function is f(x) = |x-8|/x and we want to find the limit as x approaches a value.

First, let's consider the limit as x approaches 8 from the left side, denoted as x → 8⁻. To do this, we substitute x values slightly smaller than 8 into the function and observe the output:

x → 8⁻ (x values approaching 8 from the left side):
7.9: |7.9-8|/7.9 = 0.1266...
7.99: |7.99-8|/7.99 = 0.0125...
7.999: |7.999-8|/7.999 = 0.00125...
7.9999: |7.9999-8|/7.9999 = 0.000125...

As x approaches 8 from the left side, the function approaches 0.

Next, let's consider the limit as x approaches 8 from the right side, denoted as x → 8⁺. To do this, we substitute x values slightly larger than 8 into the function and observe the output:

x → 8⁺ (x values approaching 8 from the right side):
8.1: |8.1-8|/8.1 = 0.0123...
8.01: |8.01-8|/8.01 = 0.0012...
8.001: |8.001-8|/8.001 = 0.00012...
8.0001: |8.0001-8|/8.0001 = 0.000012...

As x approaches 8 from the right side, the function also approaches 0.

Since both the left-hand limit and right-hand limit are approaching 0, we can conclude that the limit of f(x) as x approaches 8 is 0.

Therefore, the value of the limit is 0.