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If a is small in comparison with x, then...

If a is small in comparison with x, then `((x)/(x+a))^(1//3) - ((x)/(x-a))^(1//3)=`

A

`(-2a)/(3x)- (28 a^3)/(81x^3)`

B

`(2a)/(3x)-(28 a^3)/(81x^3)`

C

`(-2a)/(3x)+(28a^3)/(81 x^3)`

D

`(2a)/(3x)+(28 a^3)/( 81 x^3)`

Text Solution

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The correct Answer is:
A
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DIPTI PUBLICATION ( AP EAMET)-BINOMIAL THEOREM-EXERCISE 1C (BINOMIAL THEOREM WITH RATIONAL INDEX)
  1. If x is so small, higher powers of x may be neglected then root(3)(x^2...

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  2. If a is small in comparison with x, then ((x)/(x+a))^(1//2) + ((x)/(x-...

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  3. If a is small in comparison with x, then ((x)/(x+a))^(1//3) - ((x)/(x-...

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  4. If sqrt([(x)/(x-1)])=a0 + (a1)/( x-1) + (a2)/((x-1)^2)+…..... where x...

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  5. If (a+bx)^(-3) = (1)/(27) + (1)/(3) x + ….. then the ordered pair (a, ...

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  6. If p and q are the coefficients of x^n in (1+x)^(2n) and (1-4x)^(-1//2...

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  7. (8.8)^(1//3) =

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  8. root(3)(1003)-root(3)(997)=

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  9. 1+(1)/(4) + (1.3)/(4.8) + (1.3.5)/(4.8.12)+…...=

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  10. 1+(2)/(4) + (2.5)/(4.8)+(2.5.8)/(4.8.12)+(2.5.8.11)/(4.8.12.16)+…..=

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  11. 1+(2)/(6)+(2.5)/(6.12)+(2.5.8)/(6.12.18)+….....=

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  12. Find the sum of the infinite series (3)/(4)+(3.5)/(4.8)+(3.5.7)/(4.8...

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  13. 1+(1)/(2). (3)/(5) + (1.3)/(2.4) . (9)/(25)+(1.3.5)/(2.4.6).(27)/(125)...

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  14. The sum of the series 1+ (2)/(3)((1)/(8)) + (2 xx 5 xx 8)/(3 xx 6 xx 9...

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  15. 1+(k)/(3) + (k(k+1))/(3.6) + (k(k+1) (k+2))/(3.6.9) + …=

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  16. Find the sum of the infinite series (7)/(5)(1+(1)/(10^(2))+(1.3)/(1...

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  17. 1-(1)/(4)+(1.3)/(4.8)-(1.3.5)/(4.8.12)+…..=

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  18. 1-(1)/(5)+(1.4)/(5.10) - (1.5.7)/(5.10.15)+…..=

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  19. 1-(1)/(8)+(1.3)/(8.16)-(1.3.5)/(8.16.24)+…..=

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  20. 1-(3)/(4)+(3.5)/(4.8)-(3.5.7)/(4.8.12)+….=

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