- #1

Specter

- 120

- 8

## Homework Statement

##\frac {lim} {x→0} \frac {\sqrt {x+1}-1} {x}##

## Homework Equations

## The Attempt at a Solution

I know the limit as x approaches 0 isn't supposed to be a fraction but I can't get the x approaches 0 under the lim.

I couldn't get some of this typed out in latex, it just wouldn't work for me. But here's the rest of the work. The square root is only over the x+1's.

##\frac {lim} {x→0} \frac {\sqrt {x+1}-1} {x}##

##\frac {lim} {x→0} \frac {(√x+1 -1)(√x+1 +1)} {x(√x+1 +1)}##

##\frac {lim} {x→0} \frac {x} {x(√x+1 +1)}##

##=\frac {1} {√1+1}##

=0.5

I have a few questions. From step 2 to step 3 the numerator gets reduced only to x. I don't know how.

When multiplying the numerator by it's conjugate, does it always result in the numerator equaling 1?

For step 4, does x just get factored out of the denominator and the numerator of x just gets changed to 1?