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Mathematics: Post your doubts here!

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in ON11 P31, Q1, we found x using 'ln'. What i want to know is if there is a constant on one side do i take it as ln3 or lne^3, In this question they took ln3 while in other questions for eg, differential equations we take it as lne^3. Please Help.
Post the links!
 
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smzimran Assalamoalaikum wr wb!

I need help with the last part of the last question of Nov:2011 # 3

mark scheme

I do know how to do it...but i cant seem to get the answer...! :unsure:

it's like we take the root of 2 ± 2 root 3i

how i do is...equate that to (a + bi)^2 but..if we simplify...i get a^2 + b^2 = -2.....and this cant be solved...ms uses a^2 - b^2.....can u tell me when exactly do we use '-' b^2 ?
 
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e^x = 1 + 6e^−x
Using u = e^x
The equation becomes
u = 1 + 6/u
u^2 = u + 6
u^2 - u - 6 = 0
(u+2)(u-3) = 0
u = -2 or u = 3
e^x = -2
This cannot be solved as ln or lg of a negative number is undefined!

The only solution is
e^x = 3
x = ln3 / lne
x = ln3
x = 1.10

We take lne^x
but according to power rule, the power becomes coefficient
so lne^x = xlne
and lne = 1
so
xlne = x

See the notes i posted on logs above !
 
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Wait i'll tell you in afternoon after i solve this paper myself!

i have almost done it, but i just don't know how to remover "x" from the differential and put u into it. the differential is sec^2x and we have to use substitution u=tanx. du/dx is sec^2x but how can i just remove 'X" and replace it with U"?
 
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e^x = 1 + 6e^−x
Using u = e^x
The equation becomes
u = 1 + 6/u
u^2 = u + 6
u^2 - u - 6 = 0
(u+2)(u-3) = 0
u = -2 or u = 3
e^x = -2
This cannot be solved as ln or lg of a negative number is undefined!

The only solution is
e^x = 3
x = ln3 / lne
x = ln3
x = 1.10

We take lne^x
but according to power rule, the power becomes coefficient
so lne^x = xlne
and lne = 1
so
xlne = x

See the notes i posted on logs above !
hey could you please help me with my doubt.I've posted it twice here but haven't gotten any reply.Since you've been helping a lot of people,I am asking you.
http://www.xtremepapers.com/papers/CIE/Cambridge International A and AS Level/Mathematics (9709)/9709_w11_ms_32.pdf
On a sketch of an Argand diagram, shade the region whose points represent the complex numbers z which satisfy the inequality |z − 3i | ≤ 2. Find the greatest value of arg z for points in this region.
The question asks about greatest value of argument,sadly I don't even know the least argument value so could you just explain it to me or better if you are of any links,will u let me know?
Please do reply soon.thanks
 
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