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Mathematics: Post your doubts here!

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Guys,I am freaking out.Don't know anything in Vectors.Does anyone know any links or files which can help me understand the fundamentals?I downloaded the file from schoolworkout but that all is Russian for me.Please let me know if you have any useful notes yourself which could help.
thanks
 
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u r asked to find the coordinates means the value of x and y. u found x=2. now keep it in the equation to find y. it will be ln2 +1
so coordinate is x,y
2, ln2+1
 
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9709/32/M/J/11 Q10)iii
Need help! =]
tangent passes through point P and through the origin. at point P the x coordinate is "p". at origin it is 0. the tangent will have same gradient at both the points. take out the gradient of P by diffrenciating the equation given.
the gradient at origin will be (y-y1)/(x-x1)
at origin x and y are 0 so:
(y-0)/(x-0)
= y/x
replace y with the equation given.
equate both the gradients. u will find the value of x coordinate of p
 
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u r asked to find the coordinates means the value of x and y. u found x=2. now keep it in the equation to find y. it will be ln2 +1
so coordinate is x,y
2, ln2+1


oh yaah thats it! thanx alot! lolx I waz thinking that the next value should also be of X not thinking in terms of Y ..hehe thanx
 
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9709/33/O/N/11 Q10
Anyone?
(tanx^n+2 tanx^n)dx substitute tanx = u

(u^n+2 + u^n)dx now du = sec^2x dx

so when substituting du will give


(u^n+2 + u^n)/sec^2x du
now use identity sec^2x = 1+ tan^2x .. means (1 + U^2)

substitute this value of sec^2x in the eq. above



(u^n+2 + u^n)/ (1 + U^2)du now take U^n in numenator

U^n (U^2 + 1 )/ (1 + U^2)du now cxancel (U^2 +1)
u wil get a simple eq. (U^n)du
inegrate it
u^n+1 / n+1 now convert back into original by substiuting tanx

tanx^n+1/ n+1 put the limits
tan(45)^n+1/n+1 tan45 = 1 so... 1^n+1 = 1 :)


it wil be as follows 1/ n+1
 
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(tanx^n+2 tanx^n)dx substitute tanx = u

(u^n+2 + u^n)dx now du = sec^2x dx

so when substituting du will give


(u^n+2 + u^n)/sec^2x du
now use identity sec^2x = 1+ tan^2x .. means (1 + U^2)

substitute this value of sec^2x in the eq. above



(u^n+2 + u^n)/ (1 + U^2)du now take U^n in numenator

U^n (U^2 + 1 )/ (1 + U^2)du now cxancel (U^2 +1)
u wil get a simple eq. (U^n)du
inegrate it
u^n+1 / n+1 now convert back into original by substiuting tanx

tanx^n+1/ n+1 put the limits
tan(45)^n+1/n+1 tan45 = 1 so... 1^n+1 = 1 :)


it wil be as follows 1/ n+1



how about part b)ii its hard :(
 
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how about part b)ii its hard :(
iib) (tan9 + tan7) + (tan5+tan3) + 4(tan7+tan5)
we have the integration for tan(n) + tan(n+2).
so we will open all these according to the formula. we wrote 4(tan7+tan5) cox there are 5tan7 and 5tan5. and only one of them are used with tan9 and tan3 respectively
 
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iib) (tan9 + tan7) + (tan5+tan3) + 4(tan7+tan5)
we have the integration for tan(n) + tan(n+2).
so we will open all these according to the formula. we wrote 4(tan7+tan5) cox there are 5tan7 and 5tan5. and only one of them are used with tan9 and tan3 respectively
sorry i dint get yu :(
 
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