Functions (Limits)

**drkidd22** · July 28th 2009, 03:40 PM

So...

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

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

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

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

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

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

So...That it I'm done?

**pickslides** · July 28th 2009, 04:13 PM

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

No limit was asked?

**drkidd22** · July 28th 2009, 04:23 PM

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

**ANDS!** · July 28th 2009, 04:27 PM

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.

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

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

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

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

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

So...That it I'm done?

Are you meant to find the difference quotient?

**drkidd22** · July 28th 2009, 04:33 PM

Just says simplify completly

**drkidd22** · July 28th 2009, 04:39 PM

I'm stuck on this simplifying this one.

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

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

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

**skeeter** · July 28th 2009, 04:48 PM

Originally Posted by drkidd22

I'm stuck on this simplifying this one.

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

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

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

you're done.

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