Question

Find the limit.

Answer 1

\[\lim_{x \rightarrow 10^{+}} \frac{ \left| x-10 \right| }{ x-10 }\]

Answer 2

ooo I just took a test on this.

Answer 3

@SanjanaP please :)

Answer 4

Hold on.

Answer 5

First, recognize that by direct substitution, the limit is of the indeterminate form zero over zero.

Next, rewrite the function. Recall the definition of absolute value. Since this is a piecewise function, the limit is evaluated by considering the one-sided limits.

Answer 6

Let’s consider the limit from the left. There is a common factor of x minus ten in both the numerator and denominator. By cancelling the common factor the function is simplified to negative one.

Answer 7

Now, let’s consider the limit from the right. Again, there is a common factor of x minus ten in both the numerator and denominator. By cancelling the common factor the function is simplified to one.

Answer 8

Since you wanted it from the right, its 1.
Got your answer and explanation? @dimensionx

Answer 9

Thanks

Answer 10

You're Welcome!