2006-06-06 12:48:52 · 9 answers · asked by V 2 in Science & Mathematics ➔ Mathematics
Multiply the numerator and denominator by (√ x + ∆x ) + ( √ x )
[(√ x + ∆x ) - ( √ x )][( √ x + ∆x ) + ( √ x )]
= x + ∆x - x
= ∆x
∆x/[∆x[(√ x + ∆x ) + ( √ x )]]
= 1/[(√ x + ∆x ) + ( √ x )]
Replace ∆x with 0.
= 1/[(√ x + 0 ) + ( √ x )]
= 1/[(√ x ) + ( √ x )]
= 1/(2√ x )
2006-06-06 12:57:10 · answer #1 · answered by MsMath 7 · 7⤊ 0⤋
Use L'scientific institution rule: lim x->+0; ln x = -inf lim x->+0; a million/x = inf lim x->0; ln(x)/(a million/x) = lim x->0;(a million/x)/-(a million/x^2) = = - lim x->0; (a million/x)(a million/x^2) = = -lim x->0; a million/x * x^2 = -lim x->0; x = 0 as a effect lim x->0 x^x = lim x->0 e^(x ln(x)) = e^0 = a million
2016-10-30 08:15:17 · answer #2 · answered by belschner 4 · 0⤊ 0⤋
1 / ( 2 √ x )
2006-06-06 12:53:33 · answer #3 · answered by ymail493 5 · 0⤊ 0⤋
43
2006-06-06 12:49:57 · answer #4 · answered by jimbob92065 5 · 0⤊ 0⤋
This is the definition of the derivative of √ x, which is 1/(2√ x).
2006-06-06 12:53:26 · answer #5 · answered by just♪wondering 7 · 0⤊ 0⤋
If you're clever enough to write this equation, you should be clever enough get the answer, especially as it's so easy. Were you asleep in this class?
2006-06-06 12:52:35 · answer #6 · answered by Anonymous · 0⤊ 0⤋
huh???
Ah!
OK, if you have square root of x + delta x - square root of x, than there's only delta x!
So:
[delta x]/delta x
that would be 1!
So you have delta of x is equal to 1!
Hope I understood your question right and gave you a helpful answer!
2006-06-06 12:52:38 · answer #7 · answered by Robin 2 · 0⤊ 0⤋
the limit does not exist
2006-06-06 12:50:55 · answer #8 · answered by Shaw1Net6 4 · 0⤊ 0⤋
eleventy-million?
2006-06-06 12:52:23 · answer #9 · answered by depp_lover 7 · 0⤊ 0⤋