Question

evaluate analytically :
\frac{ sqrt{5x+5h} - sqrt{5x} }{ h }

Answer 1

I'll assume its 1st principals... with a limit

you need to multiply by 1 in a different form

\[\lim_{h \rightarrow 0} \frac{\sqrt{x + h} - \sqrt{x}}{h} \times \frac{\sqrt{x + h}+\sqrt{x}}{\sqrt{x + h} + \sqrt{x}}\]

which becomes

\[\lim_{h \rightarrow 0} \frac{x + h - x}{h(\sqrt{x + h} - \sqrt{x})}\]

which should be easy to finish...

Answer 2

i did and got the wrong answer.. idk where i went wrong

Answer 3

ok... so it becomes

\[\lim_{h \rightarrow 0} \frac{h}{h(\sqrt{x + h} + \sqrt{x})}\]

cancel the h's from the numerator and denominator

gives

\[\lim_{h \rightarrow 0} \frac{1}{\sqrt{x +h} + \sqrt{x}}\]

now apply the limit for h... subsitute h = 0

and what do you get

Answer 4

so sorry for the late response.. i didnt think you answered..
but thank you
for the help