Home
Class 12
MATHS
if f (x) = lim (x to oo) (prod(i=l)^(n )...

if `f (x) = lim _(x to oo) (prod_(i=l)^(n ) cos ((x )/(2 ^(l))))` then f '(x) is equal to:

A

`(sin x)/(x)`

B

`(x)/(sin x)`

C

`(x cos - sin x)/(x ^(2))`

D

`(sin x-x cos x)/(sin ^(2)x)`

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 L=lim_(x rarr pi)(tan(pi cos^(2)x))/((x-pi)^(2)) then (L)/(pi) is equal to:

If f(x)=((x^(l))/(x^(m)))^(l+m)((x^(m))/(x^(n)))^(m+n)((x^(n))/(x^(l)))^(n+l) then f'(x) is equal to (a) 1 (b) 0 (c) x^(l+m+n) (d) none of these

Let f(x)=lim_(n to oo) ((2 sin x)^(2n))/(3^(n)-(2 cos x)^(2n)), n in Z . Then

If f(x)=lim_(n rarr oo)n(x^((1)/(n))-1) then for x>0,y>0,f(xy) is equal to

Statement.1 : The function f (x) =lim _(xtooo) (log _(e)(1+x) -x ^(2n) sin (2x))/(1+ x ^(2n)) is discontinuous at x=1 Statement.2: L.H.L. =R.H.L.ne f (1).

If f(x)=lim_(n rarr oo)n(x^((1)/(n))-1), then f or x>0,y>0,f(xy) is equal to : f(x)f(y) (b) f(x)+f(y)f(x)-f(y)(d) none of these

We have f (x) lim_(n to oo) cos (x)/(2) cos (x)/(2^(2)) cos (x)/(2^(3)) cos (x)/(2^(4)) …… …. cos (x)/(2^(n)) = ("sin" x)/(2^(n) "sin" (x)/(2^(n))) using the identity lim_(n to oo) lim_(x to 0) f(x) equals

VK JAISWAL-CONTINUITY, DIFFERENTIABILITY AND DIFFERENTIATION-EXERCISE (SUBJECTIVE TYPE PROBLEMS)
  1. if f (x) = lim (x to oo) (prod(i=l)^(n ) cos ((x )/(2 ^(l)))) then f '...

    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

    |