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If f(x)=1-x+x^(2)-x^(3)+x^(4)+….oo then ...

If `f(x)=1-x+x^(2)-x^(3)+x^(4)+….oo` then
`int_(0)^(x)f(x)dx=`

A

log x

B

`log(1-x)`

C

`log(1+x)`

D

`log(1+x^(2))`

Text Solution

Verified by Experts

The correct Answer is:
C
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AAKASH SERIES-LOGARITHMIC SERIES -EXERCISE - II(A) (CLASS WORK)
  1. ((y-1)-(1)/(2)(y-1)^(2)+(1)/(3)(y-1)^(3)-....oo)/((a-1)-(1)/(2)(a-1)^(...

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  2. If y=x+(x^(2))/(2)+(x^(3))/(3)+....oo, then x =

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  3. If f(x)=1-x+x^(2)-x^(3)+x^(4)+….oo then int(0)^(x)f(x)dx=

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  4. (1)/(2)((1)/(5)+(1)/(7))-(1)/(4)((1)/(5^(2))+(1)/(7^(2)))+(1)/(6)((1)/...

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  5. If alpha, beta are the roots of x^(2)-px+q=0 then (alpha+beta)x-(alp...

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  6. n^(th) term of log(e )(6//5) is

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  7. log(4)2-log(8)2+log(16)2-....=

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  8. 2.4^((-1)/(4))*8^((1)/(9))*16^((-1)/(16))*32^((1)/(25))*64^((-1)/(36))...

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  9. (1)/(1.2)-(1)/(2.3)+(1)/(3.4)-(1)/(4.5)+....=

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  10. (4)/(1.3)-(6)/(2.4)+(12)/(5.7)-(14)/(6.8)+….=

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  11. (1)/(1.3)+(1)/(2.5)+(1)/(3.7)+(1)/(4.9)+...=

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  12. The 3^(rd), 4^(th), 5^(th) terms in the expansion of log(e )2 are resp...

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  13. sum(n=1)^(oo)(1)/(2n(2n+1))=

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  14. -2[(1)/(8)+(1)/(64)+(1)/(384)+…..oo]=

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  15. If |x| lt 1 then coefficient of x^(n) in log(10)(1-x) is

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  16. log(1+x+x^(2)+...oo)=

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  17. (2)/(1).(1)/(3)+(3)/(2).(1)/(9)+(4)/(3).(1)/(27)+(5)/(4).(1)/(81)+…oo=

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  18. (sqrt(2)-1)/(sqrt(2))+(3-2sqrt(2))/(4)+(5sqrt(2)-7)/(6sqrt(2))+……oo=

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  19. Assertion (A) : If x+(x^(2))/(2)+(x^(3))/(3)+………oo=log((7)/(6)) then...

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  20. If f(x)=(1)/(x+1)+(1)/(2(x+1)^(2))+(1)/(3(x+1)^(3))+…(x gt 1) and f(1...

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