Question

lim (ln(2+x)-ln2)/(x)= 1/2
x--> 0

Answer 1

\[\frac{\ln(\frac{2+x}{2})}{x}\]

Answer 2

\[\ln(1+x)/x = \ln(1+x)^{1/x}\]

Answer 3

.... typoed it already

Answer 4

no it is \[ \lim_{x \rightarrow 2} (\ln(2+X)- \ln2)\div x\]

Answer 5

Just use l'hpital's rule.

Answer 6

[ln (1 + x/2)] / x
multiply and divide by 1/2
\[1/2[\ln (1 + x/2)]/x/2\]

Answer 7

\[\ln(x+2)-\ln(x) = \ln(\frac{x+2}{x})\]

Answer 8

now putting x-> 0 it becomes a standard integral of form (ln 1)/0 which is equal to 1, so the ans is 1/2 x 1 = 1/2

Answer 9

as x-> 2 we get

ln(4/2)^(1/2) = ln(sqrt(2))

Answer 10

amistre i think im right

Answer 11

wtdu say anwar???

Answer 12

him; youre right as far as x_.0 perhaps; but the question was amended

Answer 13

yeah...

Answer 14

Why don't use L'hopital's rule? It's going to be easy peasy.

Answer 15

oh yeah but maybe he wants to show d actual method

Answer 16

we both get to ln(1+x/2)^(1/x) :)

Answer 17

no d qstn is ln (2+x) - ln2 whole upon x

Answer 18

i know; and we both got to ln(1+ x/2)^(1/x)

Answer 19

does ln 1/0 does not equal 1.

Answer 20

as x-> 2 we get ln(sqrt(2))

Answer 21

as x-> 0 we get ln(1)^(.000...0001)

Answer 22

1^(tiny number) = 1 right?

Answer 23

1 ^(any#) = 1 lol

Answer 24

yes

Answer 25

ln(1) = 0

Answer 26

This is the definition of the derivative of ln(x) at x = 2. Since the derivative of ln(x) = 1/x, at 2 you get 1/2

Answer 27

The derivative as x goes to 0 is equal to 1/2

Answer 28

I think we got the questioner confused :). @lovehap, Did you get what you asked about?

Answer 29

yes it is \[\lim_{x \rightarrow 2}(\ln(2+x)-\ln(2))/ x\]

Answer 30

\[f(x)=ln (x),f'(x)=\frac{1}{x}, f'(2)=\lim_{h\to0}\frac{ln(2+h)-ln(2)}{h}=\frac{1}{2}\]

Answer 31

thank you satellite73!

Answer 32

Dx(ln(x)) = 1/x

f'(2) = 1/2.... yes

Answer 33

welcome.

Answer 34

ok thank you!

Answer 35

Past-satellite! You'll never believe what the future has in store for you!