Home
Class 12
MATHS
If the function f(x) satisfies lim(x to ...

If the function f(x) satisfies `lim_(x to 1) (f(x)-2)/(x^(2)-1)=pi`, then `lim_(x to 1)f(x)` is equal to

A

1

B

2

C

0

D

3

Text Solution

Verified by Experts

The correct Answer is:
B
Given, `lim_(x to 1) (f(x)-2)/(x^(2)-1)=pi`
`rArr lim_(x to 1)f(x)-2=pi lim_(x to 1) (x^(2)-1)`
`therefore lim_(x to 1) f(x) =pi (1^(2)-1)+2=2`
Promotional Banner

Topper's Solved these Questions

  • CONTINUITY

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise MHT CET Corner|16 Videos

  • CONTINUITY

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise MHT CET Corner|16 Videos

  • CIRCLE AND CONICS

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise All Questions|74 Videos

  • DEFINITE INTEGRALS

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise MHT CET Corner|22 Videos

Similar Questions

Explore conceptually related problems

If the function f(x) satisfies lim_(x rarr1)(f(x)-2)/(x^(2)-1)=pi evaluate quad lim_(x rarr1)f(x)

If a differentiable function f(x) satisfies lim_(x to -1) (f(x) +1)/(x^(2)-1)=(3)/(2) Then what is lim_(x to -1) f(x) equal to ?

For the function f(x) = 2 . Find lim_(x to 1) f(x)

If f(x) is a continuous function satisfying f(x)f(1/x) =f(x)+f(1/x) and f(1) gt 0 then lim_(x to 1) f(x) is equal to

lim_(x rarr oo) (1+f(x))^(1/f(x))

Let f(x)=(1)/(1-|1-x|) . Then, what is lim_(x to 0) f(x) equal to

Let f : R toR " be a real function. The function "f" is double differentiable. If there exists "ninN" and "p inR" such that "lim_(x to oo)x^(n)f(x)=p" and there exists "lim_(x to oo)x^(n+1)f(x), "then" lim_(x to oo)x^(n+1)f'(x) is equal to

MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS-CONTINUITY-EXERCISE 2 (MISCELLANEOUS PROBLEMS)
  1. If 0 lt a lt b, " then " lim(n to oo) (a^(n)+b^(n))/(a^(n)-b^(n))

    Text Solution

    |

  2. lim(x to 0)((1+x)^(8)-1)/((1+x)^(2)-1) is equal to

    Text Solution

    |

  3. If the function f(x) satisfies lim(x to 1) (f(x)-2)/(x^(2)-1)=pi, then...

    Text Solution

    |

  4. lim(x to0) (-1)^([x]) where [.] denotes the greatest function is equal...

    Text Solution

    |

  5. If lim(x to 1) (ax^(2)+bx+c)/((x-1)^(2))=2, then (a, b, c) is

    Text Solution

    |

  6. lim(m to oo)("cos"(x)/(m))^(m) is equal to

    Text Solution

    |

  7. The value of lim( x to 3) (x^(5)-3^(5))/(x^(8)-3^(8)) is equal to

    Text Solution

    |

  8. lim(x to 0) ((1-cos 2x)(3+cosx))/(x tan 4x) is equal to

    Text Solution

    |

  9. At x=3, f(x) ={(x^(5)-243",", "if " x ne 3),(x^(3)-27",", "if " x=3):}...

    Text Solution

    |

  10. The value of f(0), if f(x)=(x tan 2x)/(sin3x sin5x) is continuous at ...

    Text Solution

    |

  11. f(x)={((5^(cosx)-1)/((pi)/(2)-x)",", x ne (pi)/(2)), (log 5"," , x =(p...

    Text Solution

    |

  12. If f(x)={((sqrt(1+px)-sqrt(1-px))/(x) ",", -1 le x lt 0),((2x+1)/(x-2...

    Text Solution

    |

  13. The function f(x)=(x^3+x^2-16 x+20)/(x-2) is not defined for x=2. In o...

    Text Solution

    |

  14. In order that the function f(x)=(x+1)^(cotx) is continuous at x = 0, t...

    Text Solution

    |

  15. if f(x) is continuous and f(9/2)=2/9 then the value if lim(x->0)f((1-c...

    Text Solution

    |

  16. If f(x)={(ax+1",", x le (pi)/(2)),(sinx+b",", x gt (pi)/(2)):} is cont...

    Text Solution

    |

  17. If f(x)={((1+2x)^(1//x)",","for " x ne 0),(e^(2)",", "for " x =0):}, t...

    Text Solution

    |

  18. If f(y)={(((e^(2y)-1)*siny)/(y^(2)),", for "y ne 0),(4,", for "y=0):}...

    Text Solution

    |

  19. If f(x)={((tanx)/(sinx)",", x ne 0),(1",", x =0):} then f(x) is

    Text Solution

    |

  20. For the function f(x)={((sin^(2)ax)/(x^(2))",","where " x ne 0),(1",",...

    Text Solution

    |