# One-sided limit question

Tags:
1. Oct 13, 2014

### squirrelschaser

1. The problem statement, all variables and given/known data

Find the $lim _{x-> -1+} sqrt(x^2-3x)-2/|x+1|$

2. Relevant equations

3. The attempt at a solution

I can only solve it using l'hopital rule and would like to know the steps of solving it without using it.

$lim _{x->-1+} (2x-3)/|1|= -5/4$

2. Oct 13, 2014

### Staff: Mentor

Multiply the expression by 1 in the form of the conjugate of the numerator over itself. The |x + 1| factor in the denominator can be replaced by x + 1, since x is to the right of -1, so x + 1 > 0. If the limit had been as x approaches -1 from the left you have to replace |x + 1| by -(x + 1).

3. Oct 13, 2014

### LCKurtz

I suppose you mean$$\lim_{x\to -1^+}\frac{\sqrt{x^2-3x}-2}{|x+1|}$$which is not what you wrote. Anyway since $x>-1$ you can write $|x+1|=x+1$. Try rationalizing the numerator and see if you can get it then.

 Mark44 must type faster than I do.

Last edited: Oct 13, 2014
4. Oct 13, 2014

### squirrelschaser

I'm dumb. Much thanks.

5. Oct 14, 2014

### HallsofIvy

Staff Emeritus
No, you are careless- that, at least, is curable!