1. ## Functions (Limits)

So...

I'm a little confused as of what I got to do here but this is what I've done so far.

$\displaystyle f(x)$ is given. Find $\displaystyle f(x+\Delta x)$.

$\displaystyle f(x) = x^2+1$

$\displaystyle (x+\Delta x)^2 + 1$

$\displaystyle (x+\Delta x)(x+\Delta x)+1$

$\displaystyle = x^2+2x\Delta x+\Delta x^2+1$

So...That it I'm done?

2. = $\displaystyle (1+\Delta) x^2+2x\Delta x+1$

3. nope, no limit asked, just said open up parentheses that why I left it like that

4. Originally Posted by drkidd22
So...

I'm a little confused as of what I got to do here but this is what I've done so far.

$\displaystyle f(x)$ is given. Find $\displaystyle f(x+\Delta x)$.

$\displaystyle f(x) = x^2+1$

$\displaystyle (x+\Delta x)^2 + 1$

$\displaystyle (x+\Delta x)(x+\Delta x)+1$

$\displaystyle = x^2+2x\Delta x+\Delta x^2+1$

So...That it I'm done?
Are you meant to find the difference quotient?

5. Just says simplify completly

6. I'm stuck on this simplifying this one.

$\displaystyle f(x)=\sqrt{x^2-1}$

$\displaystyle =\sqrt{(x+\Delta x)^2-1}$

$\displaystyle =\sqrt{x^2+2x\Delta x+\Delta x^2-1}$

7. Originally Posted by drkidd22
I'm stuck on this simplifying this one.

$\displaystyle f(x)=\sqrt{x^2-1}$

$\displaystyle =\sqrt{(x+\Delta x)^2-1}$

$\displaystyle =\sqrt{x^2+2x\Delta x+\Delta x^2-1}$
you're done.