Home
Class 12
MATHS
If the function f(x)=(x(x-2))/(x^(2)-4...

If the function
`f(x)=(x(x-2))/(x^(2)-4),xnepm2`
is continuous at x=2, then what is f(2) equal to?

A

0

B

`(1)/(2)`

C

1

D

2

Text Solution

Verified by Experts

The correct Answer is:
B
Let `f(x)=(x(x-2))/(x^(2)-4)=(x(x-2))/((x-2)(x+2))=(x)/(x+2)`
Since f(x) is continuous at x=2
`:.underset(xto0)limf(x)=f(2)`
`impliesunderset(xto2)lim(x)/(x+2)=f(2)`
`impliesf(2)=(2)/(4)=(1)/(2)`
Promotional Banner

Topper's Solved these Questions

  • DIFFERENTIAL EQUATION

    NDA PREVIOUS YEARS|Exercise MCQs|119 Videos

  • HEIGHT & DISTANCE

    NDA PREVIOUS YEARS|Exercise Math|45 Videos

Similar Questions

Explore conceptually related problems

If the function f(x)=(x(x-2))/(x^(2)-4),xnepm2 is continuous at x = 2, them what is f(2) equal to?

If the function f(x)=(3x^(2)ax+a+3)/(x^(2)+x-2) is continuous at x=-2, then the value of f(-2) is

If the function f(x)=(3x^(2)+ax+a+3)/(x^(2)+x-2) continuous at x=-2. find f(-2)

If the function f(x)=((1-x))/(2)tan.(pix)/(2) is continuous at x = 1, then f(1) is equal to

The function f(x) = (|x+2|)/(tan^(-1)(x+2)) , is continuous for

Is the function f(x)={[x^(4)+x^(2)-x+2," for "x 1]} continuous at x=1 ?

If the function f(x)=(2^(x+2)-16)/(4^(x)-16) for x!=2;-A for x=2 is continuous at x=2 then A

If the function f(x)=(x^(2)-(A+2)x+A)/(x-2), for x!=2 and f(2)=2 is continuous at x=2, then find the value of A.

If f(x)=sin^(2)x^(2) , then what is f'(x) equal to ?

If f(x) (2^(x+2)-16)/(4^(x)-2^(4)), x != 2 is continuous at x = 2 , then the value of f(2) is

NDA PREVIOUS YEARS-FUNCTIONS, LIMIT, CONTINUITY AND DIFFERENTIABILITY-MCQs
  1. If f(x)=2x+7andg(x)=x^(2)+7,x""inR, then what are values of x for whic...

    Text Solution

    |

  2. What is lim(xto0) (a^(x)-b^(x))/(x) equal to?

    Text Solution

    |

  3. If the function f(x)=(x(x-2))/(x^(2)-4),xnepm2 is continuous at x=...

    Text Solution

    |

  4. At how many points is the fucntion f(x)=[x] discontinuous?

    Text Solution

    |

  5. If f(x)=(2)/(3)x+(3)/(2),x""inR, then what is f^(-1)(x) equal to ?

    Text Solution

    |

  6. What is lim(xtooo) (sqrt(a^(2)x^(2)ax+1)sqrt(a^(2)x^(2)+1)) equal to?

    Text Solution

    |

  7. What is the value of k for which the following fucntion f(x) is contin...

    Text Solution

    |

  8. Which one of the following is correct in respect of the function f(x)=...

    Text Solution

    |

  9. Consider the following statements: I. f(x)=|x-3| is continuous at x=...

    Text Solution

    |

  10. What is lim(xto0) x^(2)sin((1)/(x)) equal to?

    Text Solution

    |

  11. What is lim(xto-2)((1+2)/(x^(3)+8))

    Text Solution

    |

  12. If f(x)f[xy]=f[x]f[y] then f[t] may be of the form:

    Text Solution

    |

  13. Which one of the following functions is differentiable for all real va...

    Text Solution

    |

  14. What is lim(xto0) (sqrt(1+x-1))/(x)

    Text Solution

    |

  15. What is lim(xto0) (2(1-cosx))/(x^(2) equal to?

    Text Solution

    |

  16. Consider the following : 1. lim(xto0) (1)/(x) exists. 2. lim(xto0)...

    Text Solution

    |

  17. Which one of the following is correct in respect of the function f(x)=...

    Text Solution

    |

  18. What is lim(xto2) (x-2)/(x^(2)-4) equal to?

    Text Solution

    |

  19. Let f:RtoR be a function whose inverse is (x+5)/(3). What is f(x) equa...

    Text Solution

    |

  20. Consider the following statements : 1. If f(x)=x^(2)andg(y)=y^(3) th...

    Text Solution

    |