Home
Class 11
MATHS
If y=1+x/(1!)+(x^2)/(2!)+(x^3)/(3!)++(x^...

If `y=1+x/(1!)+(x^2)/(2!)+(x^3)/(3!)++(x^n)/(n !),` show that `(dy)/(dx)-y+(x^n)/(n !)=0.`

Promotional Banner

Topper's Solved these Questions

  • DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS

    CENGAGE PUBLICATION|Exercise Multiple correct answers type|11 Videos
  • LINEAR INEQUALITIES

    CENGAGE PUBLICATION|Exercise All Questions|68 Videos

Similar Questions

Explore conceptually related problems

Find by the definition the differential coefficient of the following: y=1+x/(1!)+x^2/(2!)+x^3/(3!)+……+x^n/(n!) show that dy/dx-y+x^n/(n!)=0

If y = 1 + x + (x^(2))/(2!)+(x^(3))/(3!)+(x^(4))/(4!)+* * * +(x^(n))/(n!) prove that (dy)/(dx) + (x^(n))/(n!)=y*

If y=1+x+(x^2)/(2!)+(x^3)/(3!)+...+(x^n)/(n !),t h e n(dy)/(dx) is equal to (a) y (b) y+(x^n)/(n !) (c) y-(x^n)/(n !) (d) y-1-(x^n)/(n !)

If x^(m)*y^(n)=(x+y)^(m+n) , show that (dy)/(dx)=(y)/(x) .

If y=x+(x^(3))/(3)+(x^(5))/(5)+…oo , show that (dy)/(dx)=(1)/(1-x^(2)) .

If y = x + (x^(3))/(3)+(x^(5))/(5)+* * * show that (dy)/(dx) = (1) /(1 - x^(2)) .

Statement 1: The coefficient of x^n in (1+x+(x^2)/(2!)+(x^3)/(3!)++(x^n)/(n !))^3 is (3^n)/(n !) . Statement 2: The coefficient of x^n in e^(3x) is (3^n)/(n !)

If sqrt(1-x^(2n))+sqrt(1-y^(2n))=a^(n)(x^(n)-y^(n)) , prove that, (dy)/(dx)=((x)/(y))^(n-1).sqrt((1-y^(2n))/(1-x^(2n))

dy/dx + n/x y = a/x^(n)

If y=px^(n)+qx^(-n) , show that x^(2)y_(2)+xy_(1)-n^(2)y=0 .

CENGAGE PUBLICATION-LIMITS AND DERIVATIVES-All Questions
  1. If y=sqrt((1-cos2x)/(1+cos2x),)x in (0,pi/2)uu(pi/2,pi), then find (dy...

    Text Solution

    |

  2. If x=logp and y=1/p ,then (a)(d^2y)/(dx^2)-2p=0 (b) (d^2y)/(dx^2...

    Text Solution

    |

  3. If y=1+x/(1!)+(x^2)/(2!)+(x^3)/(3!)++(x^n)/(n !), show that (dy)/(dx)...

    Text Solution

    |

  4. Let y=ln(1+cosx)^2 . Then the value of (d^2y)/(dx^2)+2/(e^(y/2)) equal...

    Text Solution

    |

  5. Find (dy)/(dx)"for"y=xsinxlogxdot

    Text Solution

    |

  6. If the function f(x)=-4e^((1-x)/2)+1+x+(x^2)/2+(x^3)/3a n dg(x)=f^(-1)...

    Text Solution

    |

  7. Differentiate y=(e^x)/(1+sinx)

    Text Solution

    |

  8. Suppose that f(0)=0a n df^(prime)(0)=2, and let g(x)=f(-x+f(f(x)))dot ...

    Text Solution

    |

  9. lf y=sqrt((1-x)/(1+x)) find dy/dxand prove that (1-x^2)(dy)/(dx)+y=0

    Text Solution

    |

  10. If g(x)=(f(x))/((x-a)(x-b)(x-c)),where f(x) is a polynomial of degree ...

    Text Solution

    |

  11. If f(x) = cosx. cos2x. Cos4x. Cos8x.cos16x, then f '(pi/4) is :

    Text Solution

    |

  12. f(x)=e^(-1/x),w h e r ex >0, Let for each positive integer n ,Pn be th...

    Text Solution

    |

  13. If ai, bi in N for i 1,2,3, then coefficient of x in the determinant;|...

    Text Solution

    |

  14. If d/(dx)[(x^m-A1x^(m-1)+A2x^(m-2)-.......+(-1)^m Am)e^x]=x^m e^x , f...

    Text Solution

    |

  15. If y=|[sinx,cosx,sinx],[cosx,-sinx,cosx],[x,1, 1]| find (dy)/(dx)dot

    Text Solution

    |

  16. Let f(x)a n dg(x) be two function having finite nonzero third-order de...

    Text Solution

    |

  17. Differentiate log sinx w.r.t. sqrt(cosx).

    Text Solution

    |

  18. If cosx/2dotcosx/(2^2)dotcosx/(2^3)...oo=(sinx)/x , then find the valu...

    Text Solution

    |

  19. Differentiate tan ^(-1)(sqrt(1+x^2 )-1)/x w,r,t. tan ^(-1)x

    Text Solution

    |

  20. If 0ltx<1, then="" prove="" that="" (1-2x)="" (1-x="x^2)+(2x-4x^3)/(1-...

    Text Solution

    |