Home
Class 12
MATHS
If |x|<1 and y=1+x+x^2+\ ddotto\ oo , th...

If `|x|<1` and `y=1+x+x^2+\ ddotto\ oo` , then find the value of `(dy)/(dx)` .

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • DIFFERENTIALS, ERRORS AND APPROXIMATIONS

    RD SHARMA ENGLISH|Exercise All Questions|107 Videos

  • DIRECTION COSINES AND DIRECTION RATIOS

    RD SHARMA ENGLISH|Exercise All Questions|90 Videos

Similar Questions

Explore conceptually related problems

If f(x) = |(x + lamda,x,x),(x,x + lamda,x),(x,x,x + lamda)|, " then " f(3x) - f(x) =

If f(x) = |(1,x,x+1),(2x,x(x-1),x(x+1)),(3x(x-1),x(x-1)(x-2),x(x+1)(x-1))| , using properties of determinant, find f(2x) - f(x).

If x is a negative integer, then (a) x+|x|=0 (b) x-|x|=0 x+|x|=-2x (d) x=-|x|

If x is a positive integer, then (a) x+|x|=0 (b) x-|x|=0 (c) x+|x|=-2x (d) x=-1|x|

If x is a negative integer, then (a) x+|x|=0 (b) x-|x|=0 (c) x+|x|=-2x (d) x=-|x|

If f(x)=sgn(x)={(|x|)/x,x!=0, 0, x=0 and g(x)=f(f(x)), then at x=0,g(x) is

If {x} and [x] represent fractional and integral part of x respectively then solve the equation x-1=(x-[x])(x-{x})

Solve the following : (i) |x-2|=(x-2) " (ii) " |x+3| = -x-3 (iii) |x^(2)-x|=x^(2)-x " (iv) " |x^(2)-x-2| =2+x-x^(2)

If f(x)=|[x-2, (x-1)^2, x^3] , [(x-1), x^2, (x+1)^3] , [x,(x+1)^2, (x+2)^3]| then coefficient of x in f(x) is

If f(x)= |1 x x+1 2x x(x-1)(x+1)x3x(x-1)x(x-1)(x-2)(x+1)x(x-1)| then f(500) is equal to a. 0 b. 1 c. 500 d. -500

RD SHARMA ENGLISH-DIFFERENTIATION-All Questions
  1. If y=sin^(-1)((1-x^2)/(1+x^2))+cos^(-1)((1-x^2)/(1+x^2)) , find (dy)/(...

    Text Solution

    |

  2. If y=sec^(-1)((x+1)/(x-1))+sin^(-1)((x-1)/(x+1)),x > 0. Find (dy)/(dx)...

    Text Solution

    |

  3. If |x|<1 and y=1+x+x^2+\ ddotto\ oo , then find the value of (dy)/(...

    Text Solution

    |

  4. If u=sin^(-1)((2x)/(1+x^2)) and v=tan^(-1)((2x)/(1-x^2)) , where -1<x<...

    Text Solution

    |

  5. If f(x)=log{(u(x))/(v(x))},\ u(1)=v(1) and u^(prime)(1)=v^(prime)(1)=2...

    Text Solution

    |

  6. If y=log(3x),\ \ x!=0 , find (dy)/(dx) .

    Text Solution

    |

  7. If f(x) is an even function, then write whether f^(prime)(x) is eve...

    Text Solution

    |

  8. If f(x) is an odd function, then write whether f^(prime)(x) is even...

    Text Solution

    |

  9. Write the derivative of sinx w.r.t. cosxdot

    Text Solution

    |

  10. If f(x)=(log)(x^2)(logx) , then f^(prime)(x) at x=e is (a) 0 (b) 1 (c)...

    Text Solution

    |

  11. The differential coefficient of f(logx) with respect to x , where f(...

    Text Solution

    |

  12. The derivative of the function cot^(-1){(cos2x)^(1//2)} at x=pi//6 i...

    Text Solution

    |

  13. Differential coefficient of sec(tan^(-1)x) is (a)x/(1+x^2) (b) xsqrt...

    Text Solution

    |

  14. If y= tan^(-1)sqrt((1-sinx)/(1+sinx)), then the value of (dy)/(dx) at ...

    Text Solution

    |

  15. If y=(1+1/x)^x , then (dy)/(dx)= (a)(1+1/x)^x{log(1+1/x)-1/(x+1)} (b)...

    Text Solution

    |

  16. If x^y=e^(x-y) , then (dy)/(dx) is (a)(1+x)/(1+logx) (b) (1-logx)/(1+l...

    Text Solution

    |

  17. Given f(x)=4x^8 , then (a)f'(1/2)=f'(-1/2) (b) f(1/2)=-f'(-1/2) (c) f...

    Text Solution

    |

  18. If x=a\ cos^3theta,\ \ y=a\ sin^3theta , then sqrt(1+((dy)/(dx))^2)= ...

    Text Solution

    |

  19. If y=sin^(-1)((1-x^2)/(1+x^2)) , then (dy)/(dx)= (a)-2/(1+x^2) (b) 2/...

    Text Solution

    |

  20. The derivative of sec^(-1)(1/(2x^2-1)) with respect to sqrt(1+3x) at x...

    Text Solution

    |