Home
Class 12
MATHS
If 0ltylt2^(1//3) and x(y^(3)-1)=1 then ...

If `0ltylt2^(1//3)` and `x(y^(3)-1)=1` then
`(2)/(x)+(2)/(3x^(3))+(2)/(5x^(5))`+…=

A

`log((y^(3))/(2-y^(3)))`

B

`log((y^(3))/(1-y^(3)))`

C

`log((2y^(3))/(1-y^(3)))`

D

`log((y^(3))/(1-2y^(3)))`

Text Solution

AI Generated Solution

To solve the problem step by step, we start with the given equations and derive the required expression. ### Step 1: Understand the given equations We have two conditions: 1. \( 0 < y < 2^{1/3} \) 2. \( x(y^3 - 1) = 1 \) ### Step 2: Solve for \( x \) ...
Promotional Banner

Topper's Solved these Questions

  • EXPONENTIAL AND LOGARITHMIC SERIES

    OBJECTIVE RD SHARMA ENGLISH|Exercise Section II - Assertion Reason Type|5 Videos

  • EXPONENTIAL AND LOGARITHMIC SERIES

    OBJECTIVE RD SHARMA ENGLISH|Exercise Exercise|37 Videos

  • EXPONENTIAL AND LOGARITHMIC SERIES

    OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|20 Videos

  • ELLIPSE

    OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|29 Videos

  • HEIGHTS AND DISTANCES

    OBJECTIVE RD SHARMA ENGLISH|Exercise Exercise|45 Videos

Similar Questions

Explore conceptually related problems

If x^(2)y = 2x - y and |x| lt 1 , then (( y + (y^(3))/(3) + (y^(5))/(5) + ….oo))/((x + (x^(3))/(3) + (x^(5))/(5) + ……oo)) =

Evaluate lim_(xto0)((1+5x^(2))/(1+3x^(2)))^(1//x^(2))

If y= "tan"^(-1) (4x)/(1+5x^(2)) + "tan"^(-1) (2 + 3x)/(3-2x) , then prove that (dy)/(dx)= (5)/(1+25x^(2))

If x^3-2x^2y^2+5x+y-5=0 and y(1)=1 , then (a) y^(prime)(1)=4/3 (b) y'(1)=-4/3 (c) y''(1)=-8(22)/(27) (d) y^(prime)(1)=2/3

Solve for : 2/(x+1)+3/(2(x-2))=(23)/(5x);x!=0,-1,2

2[(1)/(2x + 1) + (1)/(3(2x + 1)^(3)) + (1)/(5(2x + 1)^(5)) + (1)/(5(2x + 1)^(5)) + …] is equal to ,

find lim_(x->1) ((x^4-3x^2+2)/(x^3-5x^2+3x+1))

Let tan^(-1)y=tan^(-1)x+tan^(-1)((2x)/(1-x^2)) , where |x|<1/(sqrt(3)) . Then a value of y is : (1) (3x-x^3)/(1-3x^2) (2) (3x+x^3)/(1-3x^2) (3) (3x-x^3)/(1+3x^2) (4) (3x+x^3)/(1+3x^2)

The image of the line (x-1)/3=(y-3)/1=(z-4)/(-5) in the plane 2x-y+z+3=0 is the line (1) (x+3)/3=(y-5)/1=(z-2)/(-5) (2) (x+3)/(-3)=(y-5)/(-1)=(z+2)/5 (3) (x-3)/3=(y+5)/1=(z-2)/(-5) (3) (x-3)/(-3)=(y+5)/(-1)=(z-2)/5

lim_(x rarr 0)((5x^2+1)/(3x^2+1))^(1//x^2)

OBJECTIVE RD SHARMA ENGLISH-EXPONENTIAL AND LOGARITHMIC SERIES-Section I - Solved Mcqs
  1. In the expansion of log(10)(1-x),|x|lt1 the coefficient of x^(n) is

    Text Solution

    |

  2. Sum of series 9/(1!)+19/(2!)+35/(3!)+57/(4!)+... (A) 7e-3 (B) 12e-5...

    Text Solution

    |

  3. The constant term in the expansion of (3^(x)-2^(x))/(x^(2)) is

    Text Solution

    |

  4. Sigma(n=1)^(oo) (x^(2n))/(2n-1) is equal to

    Text Solution

    |

  5. Then sum of the series 1+(1+3)/(2!)x+(1+3+5)/(3!)x^(2)+(1+3+5+7)/(4...

    Text Solution

    |

  6. 1/(e^(3x))(e^x+e^(5x))=a0+a1x+a2x^2+........=>2a1+2^3a3+2^5a5+......=

    Text Solution

    |

  7. Let S=x-(x^(3))/(3!)+(x^(5))/(5!)… and C=1-(x^(2))/(2!)+(x^(4))/(4!) T...

    Text Solution

    |

  8. The sum of series 2/(3!)+4/(5!)+6/(7!)+...........oo is :

    Text Solution

    |

  9. The sum of the series S=Sigma(n=1)^(infty)(1)/(n-1)! is

    Text Solution

    |

  10. The sum of the series loge(3)+(loge(3))^3/(3!)+(loge(3))^5/(5!)+....+ ...

    Text Solution

    |

  11. The value of 1+(log(e)x)+(log(e)x)^(2)/(2!)+(log(e)x)^(3)/(3!)+…inft...

    Text Solution

    |

  12. (1+3)loge3+(1+3^2)/(2!)(loge3)^2+(1+3^3)/(3!)(loge 3)^3+....oo= (a)28...

    Text Solution

    |

  13. If agt0 and x in R, then 1+(xlog(e)a)+(x^(2))/(2!)(log(e)a)^(2)+(x^(...

    Text Solution

    |

  14. (2)/(2!)+(2+4)/(3!)+(2+4+6)/(4!)+….infty is equal to

    Text Solution

    |

  15. 1+(2x)/(1!)+(3x^(2))/(2!)+(4x^(3))/(3!)+..infty is equal to

    Text Solution

    |

  16. 1/2(1/2+1/3)-1/4((1)/(2^(2))+(1)/(3^(2)))+1/6((1)/(2^(3))+(1)/(3^(3)))...

    Text Solution

    |

  17. The sum of series (1)^(2)/(1.2!)+(1^(2)+2^(2))/(2.3!)+(1^(2)+2^(2)+3...

    Text Solution

    |

  18. The sum of the series (1)/(2!)+(1)/(4!)+(1)/(6!)+..to infty is

    Text Solution

    |

  19. If 0ltylt2^(1//3) and x(y^(3)-1)=1 then (2)/(x)+(2)/(3x^(3))+(2)/(5x...

    Text Solution

    |

  20. The sum of the series (1)/(2!)+(1+2)/(3!)+(1+2+3)/(4!)+..to infty is...

    Text Solution

    |