Home
Class 12
MATHS
if f(x) =(x-e^(x)+ cos 2x)/(x^(2)),xne0...

`if f(x) =(x-e^(x)+ cos 2x)/(x^(2)),xne0` , is continuous at `x=0` , then

A

`f(0) = (5)/(2)`

B

`[f(0)] = -2`

C

`{f(0)} = - 0.5`

D

`[f(0)].{f(0)} = - 1.5`

Text Solution

Verified by Experts

The correct Answer is:
D
Promotional Banner

Topper's Solved these Questions

  • CONTINUITY AND DIFFERENTIABILITY

    ARIHANT MATHS ENGLISH|Exercise Exercise (More Than One Correct Option Type Questions)|25 Videos
  • CONTINUITY AND DIFFERENTIABILITY

    ARIHANT MATHS ENGLISH|Exercise Exercise (Statement I And Ii Type Questions)|11 Videos
  • CONTINUITY AND DIFFERENTIABILITY

    ARIHANT MATHS ENGLISH|Exercise Exercise For Session 7|9 Videos
  • COMPLEX NUMBERS

    ARIHANT MATHS ENGLISH|Exercise Complex Number Exercise 8|2 Videos
  • COORDINATE SYSTEM AND COORDINATES

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

Similar Questions

Explore conceptually related problems

If f(x) = (x-e^(x) + cos 2x)/(x^(2)), x ne 0 is continuous at x = 0, then

If f(x)=(x-e^(x)+cos2x)/(x^(2)) where x!=0 , is continuous at x=0 then (where, {.} and [x] denotes the fractional part and greatest integer)

If f(x)=(4+sin2x+a sinx+Bcosx)/(x^(2)) for x!=0 is continuous at x=0 , then A+B+f(0) is

The value of the function f at x=0 so that the function f(x)=(2^(x)-2^(-x))/(x), x ne0 , is continuous at x=0 , is

If the function f(x), defined as f(x)={{:((a(1-xsinx)+b cosx+5)/(x^(2)),":", xne0),(3,":",x=0):} is continuous at x=0 , then the value of (b^(4)+a)/(5+a) is equal to

f:R->R is defined by f(x)={(cos3x-cosx)/(x^2), x!=0lambda, x=0 and f is continuous at x=0; then lambda=

If the function f(x) = (x(e^(sinx) -1))/( 1 - cos x ) is continuous at x =0 then f(0)=

The value of k for which f(x)= {((1-cos 2x )/(x^2 )", " x ne 0 ),(k ", "x=0):} continuous at x=0, is :

If f(x)=(2x+3sinx)/(3x+2sinx) , x!=0 is continuous at x=0 , then find f(0)

If the function f(x) defined as f(x) defined as f(x)={3,x=0(1+(a x+b x^3)/(x^2))^(1/x),x >0 is continuous at x=0, then a=0 b. b=e^3 c. a=1 d. b=(log)_e3

ARIHANT MATHS ENGLISH-CONTINUITY AND DIFFERENTIABILITY-Exercise (Single Option Correct Type Questions)
  1. Let f(x) = (g(x))/(h(x)), where g and h are continuous functions on th...

    Text Solution

    |

  2. Find dy/dx if y=2x^7

    Text Solution

    |

  3. if f(x) =(x-e^(x)+ cos 2x)/(x^(2)),xne0 , is continuous at x=0 , t...

    Text Solution

    |

  4. Consider the function f(x) = {{:(x{x}+1",","if",0 le x lt 1),(2-{x}","...

    Text Solution

    |

  5. Let f(x) = {{:((2^(x)+2^(3-x) - 6)/(sqrt(2^(-x))-2^(1-x))",","if",x gt...

    Text Solution

    |

  6. Let [x] denote the integral part of x in R and g(x) = x- [x]. Let f(x...

    Text Solution

    |

  7. Let f be a differentiable function on the open interval(a, b). Which o...

    Text Solution

    |

  8. Number of points where the function f(x)=(x^2-1)|x^2-x-2| + sin(|x|) i...

    Text Solution

    |

  9. Consider function f: R - {-1,1}-> R. f(x)=x/[1-|x|] Then the incorrect...

    Text Solution

    |

  10. Find dy/dx if 2y-e^x=6

    Text Solution

    |

  11. The total number of points of non-differentiability of f(x) = min[|sin...

    Text Solution

    |

  12. The function f(x)=[x]^2-[x^2] is discontinuous at (where [gamma] is t...

    Text Solution

    |

  13. The function f(x) = (x^(2) - 1)|x^(2)-6x + 5|+cos|x| is not differenti...

    Text Solution

    |

  14. If f(x) = {{:((1)/(e^(1//x))",",x ne 0),(0",",x = 0):} then

    Text Solution

    |

  15. The function g(x) = {{:(x+b",",x lt 0),(cos x",",x ge 0):} can be made...

    Text Solution

    |

  16. The graph of function f contains the point P(1, 2) and Q(s, r). The e...

    Text Solution

    |

  17. Consider f(x)=[[2(sinx-sin^3x)+|sinx-sin^3 x|)/(2(sinx-sin^3 x)-|sinx...

    Text Solution

    |

  18. If f(x+y) = f(x) + f(y) + |x|y+xy^(2),AA x, y in R and f'(0) = 0, then

    Text Solution

    |

  19. Let f(x) = max{|x^2 - 2 |x||,|x|} and g(x) = min{|x^2 - 2|x||, |x|} th...

    Text Solution

    |

  20. about to only mathematics

    Text Solution

    |