# Finding the Limit of x^2-1/|x-1| at x=1

• n.a.s.h
In summary, the limit of x^2-1/|x-1| at x=1 is undefined due to a division by 0. Direct substitution cannot be used to find the limit at x=1. However, the expression can be simplified by factoring to (x+1) at x=1. Graphically, the limit at x=1 is represented by a vertical asymptote and may vary for different values of x.
n.a.s.h

## Homework Statement

Finding a limit? x^2-1/| x-1|?

when x approaches 1 from the right

and when x approaches 1 from the left

## The Attempt at a Solution

for the right i got 2 and left i got -2 but I am not sure...

That's right. I'd feel a little more confident that you understood it if you'd explain why.

## 1. What is the limit of x^2-1/|x-1| at x=1?

The limit of x^2-1/|x-1| at x=1 is undefined. This is because as x approaches 1 from both the left and right sides, the denominator, |x-1|, approaches 0, resulting in a division by 0 which is undefined.

## 2. Can the limit be found using direct substitution?

No, the limit cannot be found using direct substitution at x=1 because it would result in a division by 0 which is undefined.

## 3. Is there a way to simplify the expression before finding the limit?

Yes, the expression can be simplified by factoring out (x-1) from both the numerator and denominator, resulting in the limit of (x+1) at x=1.

## 4. How can graphical representation help in understanding the limit?

Graphically, the limit at x=1 can be represented by a vertical asymptote at x=1. This means that as x approaches 1 from both sides, the function approaches infinity.

## 5. Is the limit the same for all values of x?

No, the limit of x^2-1/|x-1| depends on the value of x. At x=1, the limit is undefined, but for other values of x, the limit may be a finite number.

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