Im pretty new to calculus and i have a question if anyone would care to help me. I know how to find the derivative of sqrt(x) by using the power rule. f'(x)=1/2sqrt(x) But how do i find it using the limit definition? Is the following correct.... Lim h->0 f(x)=sqrt(x) Lim h->0 f(x+h)-f(x)/h Lim h->0 f(sqrt(x+h))-f(sqrt(x))/h Is that correct? Am i to assume that both x and h are roots? Or would it be better to look at it like this... lim h->0 f(x+h)^1/2-f(x)^1/2 --------------------------- h
As i was sitting here i just realized why dont i just try it on paper and see if it fits the answer that the power rule says it is.... Im not smart at all.
Maybe I'm late for this, but try to "rationalize" the denominator: the difference of square to cancel the two square-roots. After that it's just algebra. Hope this helps :)
if 0.9999.... is 1 ( since there is no real number between them ) then is [0.999...] =1? or is 1 > 0.9999... by dx which will result in [0.999...] = 0 i am confused🙏
Thank you so much ❤
Analysis and calculus IS it thé same ??
Always has been... (Linear algebra is everywhere)
Im pretty new to calculus and i have a question if anyone would care to help me.
I know how to find the derivative of sqrt(x) by using the power rule.
f'(x)=1/2sqrt(x)
But how do i find it using the limit definition? Is the following correct....
Lim h->0 f(x)=sqrt(x)
Lim h->0 f(x+h)-f(x)/h
Lim h->0 f(sqrt(x+h))-f(sqrt(x))/h
Is that correct? Am i to assume that both x and h are roots?
Or would it be better to look at it like this...
lim h->0 f(x+h)^1/2-f(x)^1/2
---------------------------
h
As i was sitting here i just realized why dont i just try it on paper and see if it fits the answer that the power rule says it is....
Im not smart at all.
Maybe I'm late for this, but try to "rationalize" the denominator: the difference of square to cancel the two square-roots. After that it's just algebra. Hope this helps :)
if 0.9999.... is 1 ( since there is no real number between them ) then is [0.999...] =1?
or
is 1 > 0.9999... by dx which will result in [0.999...] = 0
i am confused🙏
🤩👍
Your'e also teaching us how to make videos by setting them up for editing but not actually editing!
I was wondering about that part too. He took a long pause, then he redid the explanation. :))) Maybe he forgot to cut that part out.
@Ynook He's done it in other vids. I like the rawness