Home
Class 12
MATHS
If f(x)=lim(n->oo)(tanpix^2+(x+1)^nsinx)...

If `f(x)=lim_(n->oo)(tanpix^2+(x+1)^nsinx)/(x^2+(x+1)^n)` then

A

f is continuous at x = 0

B

f is differentiable at x =0

C

f is continuous but not differentiable at x = 0

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
D
Promotional Banner

Topper's Solved these Questions

  • CONTINUITY AND DIFFERENTIABILITY

    DISHA PUBLICATION|Exercise Exercise-2 : Concept Applicator|30 Videos
  • CONTINUITY AND DIFFERENTIABILITY

    DISHA PUBLICATION|Exercise Exercise-2 : Concept Applicator|30 Videos
  • CONIC SECTIONS

    DISHA PUBLICATION|Exercise Exercise-2 : Concept Applicator|30 Videos
  • DETERMINANTS

    DISHA PUBLICATION|Exercise EXERCISE -2 CONCEPT APPLICATOR|30 Videos

Similar Questions

Explore conceptually related problems

If f(x)=lim_(n rarr oo)(tan pi x^(2)+(x+1)^(n)sin x)/(x^(2)+(x+1)^(n)) then

f(x)=lim_(n rarr oo)(tan pi x^(2)+(x+1)^(n)sin x)/(x^(2)+(x+1)^(n)), find lim_(x rarr0)f(x)

If f(x)=lim_(n->oo)((x^2+a x+1)+x^(2n)(2x^2+x+b))/(1+x^(2n))and lim_(x->+-1)f(x) exist, then The value of b is (a)-1 (b). 1 ( c.) 0 (d).2

Let f(x)=(lim)_(n->oo)(2x^(2n)sin1/x+x)/(1+x^(2n))\ then find :\ (lim)_(x->-oo)f(x)

If f(x)=lim_(n rarr oo)(x^(n)-x^(-n))/(x^(n)+x^(-n)),x>1 then int(xf(x)log(x+sqrt(1+x^(2))))/(sqrt(1+x^(2)))dx is

Let f(x)=lim_(n rarr oo)(log(2+x)-x^(2n)sin x)/(1+x^(2n)) then

Let f(x)=lim_(n->oo)(2x^(2n)sin(1/x)+x)/(1+x^(2n)) then find (a) lim_(x->oo) xf(x) (b) lim_(x->1) f(x) (c) lim_(x->0) f(x) (d) lim_(x->-oo) f(x)

Let f(x)=lim_(n rarr oo)(2x^(2n)sin\ 1/x+x)/(1+x^(2n)) then find (a) lim_(x rarr oo) x f(x) (b) lim_(x rarr 1) f(x)

DISHA PUBLICATION-CONTINUITY AND DIFFERENTIABILITY-Exercise-1 : Concept Builder(Topicwise)
  1. If f(x)={(([x]-1)/(x-1)",",xne1),(0" ,",x=1):} then f(x) is

    Text Solution

    |

  2. If f(x) = {{:( e^(x) +ax ,"for " x lt 0 ),( b(x-1) ^(2) ,"for " xge 0...

    Text Solution

    |

  3. If f(x)=lim(n->oo)(tanpix^2+(x+1)^nsinx)/(x^2+(x+1)^n) then

    Text Solution

    |

  4. If f(x)=root(3)((x^4)/|x|) ,x ne 0 and f(0)=0 is:

    Text Solution

    |

  5. Let f:R->R be a function such that f((x+y)/3)=(f(x)+f(y))/3 ,f(0) = ...

    Text Solution

    |

  6. If f(x)=sum(n=0)^oo x^n/(n!)(loga)^n, then at x = 0, f(x)

    Text Solution

    |

  7. If f(x)={:{(xe^(-(1/(|x|) + 1/x)), x ne 0),(0 , x =0 ):} then f(x) is

    Text Solution

    |

  8. If u=f(x^3),v=g(x^2),f^(prime)(x)=cosx ,a n dg^(prime)(x)=sinx ,t h e ...

    Text Solution

    |

  9. If y=((a-x)sqrt(a-x)-(b-x)sqrt(x-b))/a ,t h e n(dy)/(dx) wherever it...

    Text Solution

    |

  10. If x=(1-t^(2))/(1+t^(2)) and y=(2t)/(1+t^(2)), then (dy)/(dx) is equal...

    Text Solution

    |

  11. d/(dx)[sin^2cot^(- 1)sqrt((1-x)/(1+x))] is

    Text Solution

    |

  12. Differentiate tan^(-1)((2x)/(1-x^2)) with respect to sin^(-1)((2x)/(1+...

    Text Solution

    |

  13. If f(x) = 2 sin^(-1) sqrt(1-x) + sin^(-1)(2 sqrt(x (1-x))) where x in ...

    Text Solution

    |

  14. The derivative of sin^(-1)((2x)/(1+x^(2))) with respect to cos^(-1)((1...

    Text Solution

    |

  15. If x = sint cos2t and y = cost sin2t , then at t = pi/4, the value of ...

    Text Solution

    |

  16. If x=sectheta-costheta and y=sec^n theta- cos^n theta then show that (...

    Text Solution

    |

  17. Let y=x^3-8x+7a n dx=f(t)dot If (dy)/(dt)=2 and x=3 at t=0, then (dx)/...

    Text Solution

    |

  18. If x^y = e^(x-y) " then " dy/dx ?

    Text Solution

    |

  19. "If "y= sin x +e^(x)," then "(d^(2)x)/(dy^(2))=

    Text Solution

    |

  20. If f(x) =|log(e)|x||, then f'(x) equals

    Text Solution

    |