Home
Class 12
MATHS
Discuss the continuity of the function f...

Discuss the continuity of the function `f(x)=lim_(xto oo)(log(2+x)-x^(2n)sinx)/(1+x^(2n))` at x=1.

Text Solution

Verified by Experts

The correct Answer is:
x = 1
Promotional Banner

Topper's Solved these Questions

  • CONTINUITY AND DIFFERENTIABILITY

    ARIHANT MATHS|Exercise Exercise For Session 1|5 Videos

  • CONTINUITY AND DIFFERENTIABILITY

    ARIHANT MATHS|Exercise Exercise For Session 2|4 Videos

  • COMPLEX NUMBERS

    ARIHANT MATHS|Exercise Complex Number Exercise 8|3 Videos

  • COORDINATE SYSTEM AND COORDINATES

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

Similar Questions

Explore conceptually related problems

Discuss the continuity of the function f given by f(x) = x^3+x^2-1

Discuss the continuity of the function f(x) = {:{(x , if x > 0),(x^2, if x le0):} .

Discuss the continuity of the function defined by: f(x)={(x+2,,,,if x 0):}

Discuss the continuity of the function f(x) = {:{(x^2, x le 0),(1-x,x>0):} at x = 0

Discuss the continuity of the function f(x) = {{:((|x - 2|)/(2 - x)"," ,x != 2),(-1",", x = 2):} at x = 2 .

Discuss the continuity of the function: f(x) = {:{(1+x^2,0lexle1),(2-x,x>1):} at x =1

Discuss the continuity of the function : f(x) = {:{((|x-a|)/(x-a), when x nea),(1,when x=a):} at x = a

Discuss the continuity of f(x)in[0,2],w h e r ef(x)=(lim)_(n->oo)(sin (pix/2))^(2n)

Discuss the continuity of the function (x) at x = 1 if f(x) = {{:((x - 1)/(sqrt(x^2) - 1)"," ,x != 1),(0",", x = 1):}

Discuss the continuity of the function f(x), where f(x)= {:{(2-x, x < 0),(2+x,xge0):} , at x = 2,0 and -2.

ARIHANT MATHS-CONTINUITY AND DIFFERENTIABILITY-Exercise (Questions Asked In Previous 13 Years Exam)
  1. Discuss the continuity of the function f(x)=lim(xto oo)(log(2+x)-x^(2n...

    Text Solution

    |

  2. For every pair of continuous function f, g : [0, 1] rarr R such that m...

    Text Solution

    |

  3. Let f: R to R and g:R to R be respectively given by f(x) =|x|+1 and g...

    Text Solution

    |

  4. Let f(x)={x^2|(cos)pi/x|, x!=0 and 0,x=0,x in RR, then f is a. differ...

    Text Solution

    |

  5. Q. For every integer n, leta(n) and b(n) be real numbers. Let functio...

    Text Solution

    |

  6. Let f:R->R be a function such that f(x+y)=f(x)+f(y),AA x, y in R. a. ...

    Text Solution

    |

  7. If f(x) ={{:(-x=(pi)/(2),xle -(pi)/(2)), (- cos x, -(pi)/(2)lt x ,le ...

    Text Solution

    |

  8. For the function f(x)=x cos ""1/x, x ge 1 which one of the following i...

    Text Solution

    |

  9. If lim(xtooo)((x^(2)+x+1)/(x+1)-ax-b)=4, then

    Text Solution

    |

  10. Let fandg be real valued functions defined on interval (-1,1) such tha...

    Text Solution

    |

  11. If f(x)=x-[x], where [x] is the greatest integer less than or equal to...

    Text Solution

    |

  12. Check the differentiability if f(x) = min. {1, x^(2), x^(3)}.

    Text Solution

    |

  13. Fill in the blank, in the statement given below. Let f(x) = x|x The ...

    Text Solution

    |

  14. lf is a differentiable function satisfying f(1/n)=0,AA n>=1,n in I, th...

    Text Solution

    |

  15. The domain of the derivative of the function f(x)={{:(tan^(-1)x ,if|x|...

    Text Solution

    |

  16. The left hand derivative of f(x) = [x] sin (pi x)"at x" = k is an inte...

    Text Solution

    |

  17. Which of the following functions is differentiable at x = 0 ?

    Text Solution

    |

  18. For x in R, f(x) =|log(e) 2-sinx| and g(x) = f(f(x)) , then

    Text Solution

    |

  19. If the function g(X) ={{:( ksqrt ( x+1), 0 le x le 3),( mx+2, 3 lt x...

    Text Solution

    |

  20. If f and g are differentiable functions in [0, 1] satisfying f(0)""=""...

    Text Solution

    |

  21. The function f(x) = [x] cos((2x-1)/2) pi where [ ] denotes the greate...

    Text Solution

    |