Home
Class 12
MATHS
If f(x)=(4+x)^(n),"n" epsilonN and f^(r)...

If `f(x)=(4+x)^(n),"n" epsilonN` and `f^(r)(0)` represents the `r^(th)` derivative of `f(x)` at `x=0`, then the value of `sum_(r=0)^(oo)((f^(r)(0)))/(r!)` is equal to

A

`2 ^(n)`

B

`3 ^(n)`

C

`5 ^(n)`

D

`4 ^(n)`

Text Solution

Verified by Experts

The correct Answer is:
C
Promotional Banner

Topper's Solved these Questions

  • CONTINUITY, DIFFERENTIABILITY AND DIFFERENTIATION

    VK JAISWAL|Exercise EXERCISE (ONE OR MORE THAN ONE ANSWER IS/ARE CORRECT)|36 Videos
  • CONTINUITY, DIFFERENTIABILITY AND DIFFERENTIATION

    VK JAISWAL|Exercise EXERCISE (COMPREHENSION TYPE PROBLEMS)|32 Videos
  • COMPOUND ANGLES

    VK JAISWAL|Exercise Exercise-5 : Subjective Type Problems|31 Videos
  • DETERMINANTS

    VK JAISWAL|Exercise EXERCISE-4 : SUBJECTIVE TYPE PROBLEMS|11 Videos

Similar Questions

Explore conceptually related problems

If f:R rarr R,f(x)=x+sin x, then value of int_(0)^( pi)(f^(-1)(x))dx equals

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

A derivable function f : R^(+) rarr R satisfies the condition f(x) - f(y) ge log((x)/(y)) + x - y, AA x, y in R^(+) . If g denotes the derivative of f, then the value of the sum sum_(n=1)^(100) g((1)/(n)) is

Let F(x)= F(x)=int_0^xtf(t)dt] and F(x^2)=x^4+x^5 then find the value of sum_(r=1)^12f(r^2)

Let f: R - {0} to R be defined by f(x) = x+ 1/x , then 7 + f((x))^(4) -f(x^(4)) - 4(f(x))^(2) is equal to……….

Let f(n)=sum_(r=0)^(n)sum_(k=r)^(n)([kr]). Also if f(n)=2047 ,then find the value of n

Let f:R to R differerntiable at x=0 and satisfies f(0)=0 and f'(0)=1, then the value of lim_(x to 0) (1)/(x) sum_(x to 1)^(oo) (-1)^(n) f((x)/(n))is

If a=(e^(2 pi i))/(7) and f(x)=A_(0)+sum_(k=1)^(20)A_(k)x^(k) then the value of sum_(r=0)^(6)f(a^(r)x)=n(A_(0)+A_(n)x^(n)+A_(2n)x^(2n)), then the value of n is

VK JAISWAL-CONTINUITY, DIFFERENTIABILITY AND DIFFERENTIATION-EXERCISE (SUBJECTIVE TYPE PROBLEMS)
  1. If f(x)=(4+x)^(n),"n" epsilonN and f^(r)(0) represents the r^(th) deri...

    Text Solution

    |

  2. Let f (x)= {{:(ac (x-1)+b,,, x lt 1),( x+2,,, 1 le x le 3),(px ^(2) +q...

    Text Solution

    |

  3. If y= sin (8 sin ^(-1) x ) then (1-x ^(2)) (d^(2)y)/(dx ^(2))-x (dy)/...

    Text Solution

    |

  4. If y ^(2) =4ax, then (d^(2) y)/(dx ^(2))=(ka ^(2))/( y ^(2)), where k ...

    Text Solution

    |

  5. The number of values of x , x I [-2,3] where f (x) =[x ^(2)] sin (pix)...

    Text Solution

    |

  6. If f (x) is continous and fifferentiable in [-3,9] and f'(x) in [-2,8]...

    Text Solution

    |

  7. In f (x)= [{:(cos x ^(2),, x lt 0), ( sin x ^(3) -|x ^(3)-1|,, x ge 0)...

    Text Solution

    |

  8. Let f (x) =x ^(2) +ax+3 and g (x) =x+b, where F (x) =lim (xto oo) (f(x...

    Text Solution

    |

  9. Let f (x)= {{:(2-x"," , -3 le x le 0),( x-2"," , 0 lt x lt 4):} Then f...

    Text Solution

    |

  10. If f (x) +2 f (1-x)( =x ^(2) +2AA x in R and f (x) is a differentiable...

    Text Solution

    |

  11. Let f (x)= signum (x) and g (x) =x (x ^(2) -10x+21), then the number o...

    Text Solution

    |

  12. If (d^(2))/(d x ^(2))((sin ^(4)x+ sin ^(2)x+1)/(sin ^(2)x + si n x+1))...

    Text Solution

    |

  13. f (x) =a cos (piy)+b, f'((1)/(2))=pi and int (1//2)^(3//2) f (x) dx =2...

    Text Solution

    |

  14. Let alpha (x) = f(x) -f (2x) and beta (x) =f (x) -f (4x) and alpha '(1...

    Text Solution

    |

  15. Let f (x) =-4.e ^((1-x)/(2))+ (x ^(3))/(3 ) + (x ^(2))/(2)+ x+1 and g ...

    Text Solution

    |

  16. If y=3^(2 sin ^(-1)) then |((x ^(2) -1) y ^(+) +xy')/(y)| is equal to

    Text Solution

    |

  17. Let f (x)=x+ (x ^(2))/(2 )+ (x ^(3))/(3 )+ (x ^(4))/(4 ) +(x ^(5))/(5)...

    Text Solution

    |

  18. In f (x)= [{:(cos x ^(2),, x lt 0), ( sin x ^(3) -|x ^(3)-1|,, x ge 0)...

    Text Solution

    |

  19. Let f :R to R be a differentiable function satisfying: f (xy) =(f(x)...

    Text Solution

    |

  20. For the curve sin x + si y=1 lying in the first quadrant there exist a...

    Text Solution

    |

  21. Let f (x) = x tan ^(-1) (x^(2)) + x^(4) Let f ^(k) (x) denotes k ^(th)...

    Text Solution

    |