Home
Class 12
MATHS
if f(x) = x +x^2/1! + x^3/3! +---+ x^n/n...

if `f(x) = x +x^2/1! + x^3/3! +---+ x^n/n! then f(0) + f'(0) + f''(0) + -------f''^---n times (0)` is equal to

A

`(n(n+1))/(2)`

B

`((n^(2)+1))/(2)`

C

`((n(n+1))/(2))^(2)`

D

`(n(n+1)(2n+1))/(6)`

Text Solution

Verified by Experts

The correct Answer is:
A
Promotional Banner

Topper's Solved these Questions

  • DIFFERENTIATION

    ARIHANT MATHS|Exercise Exercise (Statement I And Ii Type Questions)|10 Videos

  • DIFFERENTIATION

    ARIHANT MATHS|Exercise Exercise (Passage Based Questions)|16 Videos

  • DIFFERENTIATION

    ARIHANT MATHS|Exercise Exercise For Session 10|4 Videos

  • DIFFERENTIAL EQUATION

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|26 Videos

  • DY / DX AS A RATE MEASURER AND TANGENTS, NORMALS

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|7 Videos

Similar Questions

Explore conceptually related problems

If f(x) =x + x^(2)/(2!) + x^(3)/(3!) + ……+x^(n)/((n-1)!) , then f(0) + f^(1)(0) + f^(2)(0) +…………+f^(n)(0) is equal to:

if quad f(x)=x+(x^(2))/(1)!+(x^(3))/(3)!+--+(x^(n))/(n)! then f(0)+f'(0)+f''(0)+ is equal to

If f(x)=(a-n^(n))^(1//n) where a gt 0 and n in N , then f[f(x)] is equal to :

If f(a+x)=f(x), then int_(0)^(na)f(x)dx is equal to n in N

Let f(x)=1/(1+e^(1/x))for\ x!=0\ a n d\ f(0)=0 , then f(0^+) does not exist b. f(0) is equal to zero c. f^(prime)(0^-)\ is equal to 1 d. f^(prime)(0^+) is equal to zero

If f'(x)=(1)/((1+x^(2))^(3//2)) and f(0)=0, then f(1) is equal to :

If f'(x)=8x^(3)+3x^(2)-10x-k " and " f(0)=-3,f(-1)=0," then " f(x)= is

ARIHANT MATHS-DIFFERENTIATION -Exercise (More Than One Correct Option Type Questions)
  1. If f and g are the function whose graphs are as shown, let u(x)=f(g(x)...

    Text Solution

    |

  2. f'(x) = g(x) and g'(x) =-f(x) for all real x and f(5)=2=f'(5) then f^2...

    Text Solution

    |

  3. if f(x) = x +x^2/1! + x^3/3! +---+ x^n/n! then f(0) + f'(0) + f''(0) ...

    Text Solution

    |

  4. If y=(f(0)f(0)f)(x)andf(0)=0,f'(0)=2 then y'(0) is equal to

    Text Solution

    |

  5. If y^2=P(x) is a polynomial of degree 3, then 2(d/(dx))(y^2dot(d^2y)/(...

    Text Solution

    |

  6. If y=f(x)andx=g(y) are inverse functions of each other, then

    Text Solution

    |

  7. If y is a function of x then (d^2y)/(dx^2)+y \ dy/dx=0. If x is a func...

    Text Solution

    |

  8. Leg g(x)=ln(f(x)), whre f(x) is a twice differentiable positive functi...

    Text Solution

    |

  9. If the function f(x)=x^(3)+e^(x//2)andg(x)=f^(-1)(x), then the value ...

    Text Solution

    |

  10. If f(theta) = sin(tan^(-1)(sintheta/sqrt(cos2theta))), where -pi/4 lt ...

    Text Solution

    |

  11. If y=log(sinx)(tanx), then (dy)/ (dx) at x=(1)/(4) is equal to

    Text Solution

    |

  12. If y=sum(r=1)^(x) tan^(-1)((1)/(1+r+r^(2))), then (dy)/(dx) is equal t...

    Text Solution

    |

  13. If y=(sin^(-1)(sinalphasinx)/(1-cosalphasinx)), then y'(0) is equal to

    Text Solution

    |

  14. If f(x)=cot^(-1)((x^(x)-x^(-x))/(2)) then f'(1) equals

    Text Solution

    |

  15. The function f(x)=e^x+x , being differentiable and one-to-one, has a d...

    Text Solution

    |

  16. If f^(x)=-f(x) and g(x)=f^(prime)(x) and F(x)=(f(x/2))^2+(g(x/2))^2 an...

    Text Solution

    |

  17. If x=sectheta-costhetaandy=sec^(n)theta-cos^(n)theta, then (x^(2)+4 )(...

    Text Solution

    |

  18. If x=f(t)cost-f^(prime)(t)sint and y=f(t)sint+f^(prime)(t)cost , then ...

    Text Solution

    |

  19. If y=at^2+2bt-cand t = ax^2+2bx+c, then(d^3y)/(dx^3) equals

    Text Solution

    |

  20. Differential coefficient of (x^((l+m)/(m-n)))^(1//(n-l))*(x^((m+n)/(n-...

    Text Solution

    |