Home
Class 12
MATHS
If f(x)=x^(n),"n" epsilon N, then the va...

If `f(x)=x^(n),"n" epsilon N`, then the value of `f(1)-(f^(')(1))/(1!)+(f^(")(1))/(2!)-(f^''')(1)/(3!)+…+(-1)^(n)(f^(n)(1))/(n!)` is

A

n

B

`2^(n)`

C

`2^(n-1)`

D

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

Text Solution

Verified by Experts

The correct Answer is:
B
We have,
`f(x)=x^(n)`
`implies" "f^(r)(x)=(n!)/((n-r)!)x^(n-r),r=1,2,3...n.`
`implies" "f^(r)(1)=(n!)/((n-r)!)=""^(n)C_(r).r!`
`implies" "(f^(r)(1))/(r!)=""^(n)C_(r)`
`:." "f(1)+(f'(1))/(1!)+(f''(1))/(2!)+(f'''(1))/(3!)+...+(f^((n))(1))/(n!)=underset(r-0)overset(n)sum""^(n)C_(r)=2^(n)`
Promotional Banner

Topper's Solved these Questions

  • DIFFERENTIATION

    OBJECTIVE RD SHARMA ENGLISH|Exercise Section I - Solved Mcqs|92 Videos

  • DIFFERENTIATION

    OBJECTIVE RD SHARMA ENGLISH|Exercise Exercise|58 Videos

  • DIFFERENTIALS, ERRORS AND APPROXIMATIONS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Exercise|17 Videos

  • ELLIPSE

    OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|29 Videos

Similar Questions

Explore conceptually related problems

if f(x) = x^n then the value of f(1) - (f'(1))/(1!) + (f''(1))/(2!) + ---+((-1)^n f''^--n times (1))/(n!)

If f(x)=(1-x)^n, then the value of f(0)+f^(prime)(0)+(f^('')(0))/(2!)+(f^(''')(0))/(3!)+......(f^n(0))/(n !)dot

If f(x)=(1+x)^2, then the value of f(x0)+f^(prime)(0) +(f^(0))/(2!)+(f^(0))/(3!)+(f^n(0))/(n !)dot

If f(x)=(1+x)^2, then the value of f(x0)+f^(prime)(0) +(f^(0))/(2!)+(f^(0))/(3!)+(f^n(0))/(n !)dot

If f(x)=(a^x)/(a^x+sqrt(a ,)),(a >0), then find the value of sum_(r=1)^(2n1)2f(r/(2n))

If f(alpha)=f(beta) and n in N , then the value of int_alpha^beta (g(f(x)))^n g\'(f(x))*f\'(x)dx= (A) 1 (B) 0 (C) (beta^(n+1)-alpha^(n+1))/(n+1) (D) none of these

If f(x) = alphax^(n) prove that alpha = (f'(1))/n

If f(x) = (a-x^n)^(1/n), a > 0 and n in N , then prove that f(f(x)) = x for all x.

If f(x)=prod_(n=1)^(100)(x-n)^(n(101-n)) ; then (f(101))/(f'(101))=

If f(x)=alphax^n , prove that alpha=(f^(prime)(1))/n .

OBJECTIVE RD SHARMA ENGLISH-DIFFERENTIATION-Chapter Test
  1. If f(x)=x^(n),"n" epsilon N, then the value of f(1)-(f^(')(1))/(1!)+(f...

    Text Solution

    |

  2. If f(x)=log(e)[log(e)x], then what is f' (e) equal to?

    Text Solution

    |

  3. If e^y+xy=e then the value of (d^2y)/(dx^2) for x=0 is

    Text Solution

    |

  4. If sqrt(x+y) +sqrt(y-x)=5, then (d^(2)y)/(dx ^(2))=

    Text Solution

    |

  5. "If "ax^(2)+2hxy+by^(2)=1," then "(d^(2)y)/(dx^(2)) is

    Text Solution

    |

  6. If f(x)=sin{(pi)/(2)[x]-x^(5)},1ltxlt2 and [.] denotes the greatest in...

    Text Solution

    |

  7. f(x) is a polynomial of degree

    Text Solution

    |

  8. If y=sin(log(e)x), then x^(2)(d^(2)y)/(dx^(2))+x(dy)/(dx) is equal to

    Text Solution

    |

  9. If f(x)=(1-x)^n, then the value of f(0)+f^(prime)(0)+(f^('')(0))/(2!)+...

    Text Solution

    |

  10. "If "xsqrt(1+y)+ysqrt(1+x)=0," prove that "(dy)/(dx)=-(1)/((x+1)^(2)).

    Text Solution

    |

  11. If 8f(x)+6f(1/x)=x+5 and y=x^2(f(x), then (dy)/(dx) at x=-1 is equal t...

    Text Solution

    |

  12. If y=sin^(-1){(5x+12 sqrt(1-x^(2)))/(13)}, find (dy)/(dx).

    Text Solution

    |

  13. If f(x)=cos^(-1){(1-(log(e)x)^(2))/(1+(log(e)x)^(2))}, then f'( e )

    Text Solution

    |

  14. y=sin^(-1)[sqrt(x-ax)-sqrt(a-ax)]

    Text Solution

    |

  15. Let f(x)=(x^3+2)^(30) If f^n (x) is a polynomial of degree 20 where f^...

    Text Solution

    |

  16. If f(x)=cos^(2)x+cos^(2)(x+(pi)/(3))+sinxsin(x+(pi)/(3)) and g((5)/(4)...

    Text Solution

    |

  17. If f(x)=10cosx+(13+2x)sinx then f''(x)+f(x)=

    Text Solution

    |

  18. Let a function f:RtoR satisfy the equation f(x+y)=f(x)=f(Y)AAx, yepsil...

    Text Solution

    |

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

    Text Solution

    |

  20. If f'(x)=arc tan((x^(x)-x^(-x))/(2)), then f'(1) is equal to

    Text Solution

    |

  21. Let f(x)=2^(2x-1)" and "g(x)=-2^(x)+2xlog2. Then the set of points sat...

    Text Solution

    |