Limit of a Function with Radicals in the Numerator

[cphill29]

Homework Statement

Limit as h approaches 0 for [rad(5+h)-rad(5-h)]/h

Homework Equations

The Attempt at a Solution

limit as h approaches 0 for [(5+h)-(5-h)]/h[rad(5+h)+rad(5-h)]

limit as h approaches 0 for 2h/h[rad(5+h)+rad(5-h)]

limit as h approaches 0 for h/[rad(5+h)+rad(5-h)]

This was as far as I could get. Sorry if it's a little messy.

 

[symbolipoint]

Limit as h approaches 0 for [rad(5+h)-rad(5-h)]/h

That is Lim_(h to 0) $\frac{\sqrt{5+h} - \sqrt{5-h}}{h}$

Multiply numerator and denominator by $\sqrt{5+h} + \sqrt{5-h}$
When you work through steps, you obtain expression,...
$\frac{2}{\sqrt{5+h} + \sqrt{5-h}}$

As h approaches 0, the expression approaches $\frac{2}{\sqrt{5} + \sqrt{5}}$

Simplifying to $\frac{\sqrt{5}}{5}$. DONE.

Note minor TEX/LATEX learning problems, "Lim as h approaches 0"

 

[cphill29]

Thank you for clearing that up. Instead of cancelling the 'h', I canceled the 2 by mistake.