Question

Let f(x) = 1/(3x)^1/2 . Compute lim h→0 (f(5 + h) − f(5))/h .

Answer 1

I just need help simplfying the fraction after i plug in 5+h and 5

Answer 2

After I plug it in the definition of derivative I get (1/(15+3h)^1/2)-(1/(15)^1/2))/h

Answer 3

Ooo this one is a bit of a stinker >.<

Answer 4

\[\Large\rm \lim_{h\to0}\frac{\frac{1}{\sqrt{15+3h}}-\frac{1}{\sqrt{15}}}{h}\]

Answer 5

I tried combining the fractions and getting \[\frac{ \frac{ \sqrt{15}-\sqrt{15+3h} }{ \sqrt{15}\sqrt{15+3h} } }{ h }\]

Answer 6

but because there are so many radicals, I'm having trouble taking this equation any further

Answer 7

\[\frac{1}{h} \frac{\sqrt{15}-\sqrt{15+3h}}{\sqrt{15}\sqrt{15+3h}} \cdot \frac{\sqrt{15}+\sqrt{15+3h}}{\sqrt{15}+\sqrt{15+3h}}\]
try this...

Answer 8

\(\large\tt \color{black}{\lim_{h\to0}\dfrac{\dfrac{1}{\sqrt{15+3h}}-\dfrac{1}{\sqrt{15}}}{h}}\)

\(\large\tt \color{black}{\lim_{h\to0}\dfrac{\dfrac{\sqrt{15}-(\sqrt{15+3h})}{(\sqrt{15})\sqrt{15+3h}}}{h}}\)

\(\large\tt \color{black}{\lim_{h\to0}\dfrac{\dfrac{\sqrt{15}-(\sqrt{15+3h})}{(3)\sqrt{5(5+h)}}}{h}}\)

\(\large\tt \color{black}{\lim_{h\to0}\dfrac{\dfrac{\sqrt{15}-(\sqrt{15+3h})}{(3)\sqrt{5(5+h)}}\times \dfrac{\sqrt{15}+(\sqrt{15+3h})}{(\sqrt{15}+(\sqrt{15+3h})}}{h}}\)

\(\large\tt \color{black}{\lim_{h\to0}\dfrac{\dfrac{-h}{\sqrt{5(5+h)}(\sqrt{15}+(\sqrt{15+3h})}}{h}}\)

\(\large\tt \color{black}{\lim_{h\to0}\dfrac{-1}{\sqrt{5(5+h)}(\sqrt{15}+(\sqrt{15+3h})}}\)

\(\large\tt \color{black}{=\dfrac{-1}{\sqrt{5(5+0)}(\sqrt{15}+(\sqrt{15+3\times 0})}}\)

\(\large\tt \color{black}{=\dfrac{-1}{10\sqrt{15}}}\)

Answer 9

Oh wow! THANK YOU SO MUCH!!!!!!!!!

Answer 10

Sorry had to go for a bit :c
Looks like you've got it figured out though c: yay

Answer 11

y w