Question

how we can solve this?

Answer 1

\[\lim\frac{ \sqrt{h+4}-2 }{ h }\]

Answer 2

prolly has to do with a conjugate

Answer 3

and what is the limit "approaching"?

Answer 4

\[h \rightarrow0\]

Answer 5

multiply top and bottom by a useful form of 1: conjugate/conjugate

that will put something other than an h in the bottom to retain.

Answer 6

with any luck

Answer 7

does that make sense?

Answer 8

\[g(x)=1+\sqrt{x}\]
g'(4)=?

Answer 9

i take it thats your original problem ... and you got it to f(x+h)-f(x) over h and got stuck

Answer 10

\[\lim_{h\to 0}\frac{1+\sqrt{x+h}-1-\sqrt{x}}{h}\]
\[\lim_{h\to 0}\frac{\sqrt{x+h}-\sqrt{x}}{h}\]
is what i get to before applying a conjugate

Answer 11

and then you applied x=4 and i see your leading setup :)

still need to work out the conjugate parts then

Answer 12

g'(4)=1/4 ?

Answer 13

yep

Answer 14

thanks

Answer 15

youre welcome