Question

lim (x->a) of [f(x)-f(a)]/sqrt(x)-sqrt(a).

Interpret the following limit as the derivative of a function; use the derivative of a function to evaluate the limit.

So I've attempted it and the first thing I did was multiply by the conjugate, and after simplification I got f'(x) times (sqrt(x)+sqrt(a)). Not sure if I'm on the right path..

Answer 1

\[\lim_{x \rightarrow a}[f(x)-f(a)]/[\sqrt{x}-\sqrt{a}]\]

Answer 2

lets go 1 step before u got f'(x) times (sqrt(x)+sqrt(a)) .
you would have got \(\lim \limits_{x \rightarrow a}[f(x)-f(a)][\sqrt{x}+\sqrt{a}]/(x-a)\)
right ??

Answer 3

yeah, except the (x-a) would be under everything

Answer 4

yes, i meant that only,
now before you write f'(x)
i would ask you to split the limit into 2 products, the one which you'll evaluate as f'(x) by definition and the other as \(\lim \limits_{x->a}(\sqrt x+\sqrt a)\)

Answer 5

even the limit as (x-->a) would go away because that's part of the limit definition. So all you'd be left with is just f'(a)(2sqrt(a))

Answer 6

yeah, exactly. So would that be the end of the answer then?

Answer 7

yes, your final answer is correct , and yes that the end.
my point was just to show you to split the limit...

Answer 8

oh no that basically got me to the end! thanks a lot man

Answer 9

welcome :)