Home
Class 12
MATHS
Let f(x) = x + 2, where x le 1 and f(x) ...

Let f(x) = x + 2, where `x le 1 and f(x) = 4x - 1`, when `x gt 1`, then :

A

f(x) is discontinuous at x = 0

B

f(x) is continuous at x = 1

C

`lim_(x rarr 1) f(x) = 4`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
B
Promotional Banner

Topper's Solved these Questions

  • LIMIT AND CONTINUITY

    MODERN PUBLICATION|Exercise LATEST QUESTIONS FROM AIEEE/JEE EXAMINATIONS|11 Videos

  • LIMIT AND CONTINUITY

    MODERN PUBLICATION|Exercise QUESTIONS FROM KARNATAKA CET & COMED|7 Videos

  • LIMIT AND CONTINUITY

    MODERN PUBLICATION|Exercise QUESTIONS FROM KARNATAKA CET & COMED|7 Videos

  • INVERSE TRIGONOMETRIC FUNCTIONS

    MODERN PUBLICATION|Exercise QUESTION FROM KARNATAKA CET & COMED|10 Videos

  • MATHEMATICAL REASONING

    MODERN PUBLICATION|Exercise QUESTIONS FROM KARNATAKA CET & COMED|9 Videos

Similar Questions

Explore conceptually related problems

Let f(x) = x - 1/x , then f' (-1) is

If f(x) = 4x - x^2 , then f (a + 1) - f( a - 1) =

Let f(x) = ( 2x+1)/(1-3x) , then f^-1 (x) =

f(x) = (|x-a|)/(x-a) , when x ne a, = 1 , when x = a, then :

Let f(x)=(x)/(1+x)-log(1+x) , when x gt 0 , then f is :

Let F(x) = f(x) + f(1/x) , where , f(x) = int_1^x (log t)/(1 + t) dt . Then F(e ) equals :

Let f(x) = 1-x^5 , then f(x).f(1/x) =

Let f(x) = x-[x], x in R then f^(')(1/2) is

Let g(x) = int_0^(x) f(t) dt , where 1/2 le f(t) < 1, t in [0,1] and 0 < f(t) le 1/2 "for" t in[1,2] . Then :

Let f(x), g(x) be differentiable functions and f(1) = g(1) = 2, then : lim_(x rarr 1) (f(1) g(x) - f(x) g(1) - f(1) + g(1))/(g(x) - f(x)) equals :

MODERN PUBLICATION-LIMIT AND CONTINUITY -MULTIPLE CHOICE QUESTIONS(LEVEL - II )
  1. The value of x, where the function : f(x) = (tan x log (x-2))/(x^(2) -...

    Text Solution

    |

  2. Let f(x) = (tan ((pi)/(4) - x))/(cot 2 x), x ne pi//4, the value which...

    Text Solution

    |

  3. Let f(x) = x + 2, where x le 1 and f(x) = 4x - 1, when x gt 1, then :

    Text Solution

    |

  4. Let the function f be defined by f(x) = "x sin" (1)/(x), when x ne 0 =...

    Text Solution

    |

  5. f(x) = (|x-a|)/(x-a), when x ne a, = 1, when x = a, then :

    Text Solution

    |

  6. The value of f(0) for which the function : (log(e) (1-ax) - log(3) (1-...

    Text Solution

    |

  7. If f(x) = ((e^(x)-1)^(4))/(sin((x^(2))/(lambda^(2)))log(1+(x^(2))/(2))...

    Text Solution

    |

  8. If f(x) = [x] + [-x], x ne 2 = lambda, x = 2, then f is continuous at ...

    Text Solution

    |

  9. Let f(x) be defined by f(x) = {{:((|x^(2) - x|)/(x^(2) - x),x ne 0"," ...

    Text Solution

    |

  10. lim(x rarr oo) ((x^(2) + 5x + 3)/(x^(2) + x + 2))^(x) is :

    Text Solution

    |

  11. lim(x rarr 0) (log (3 + x) - log(3 - x))/(x) = k, the value of k is :

    Text Solution

    |

  12. lim(x rarr (pi)/(2)) ((1 - tan x//2)(1-sin x))/((1+tan x//2) (pi - 2x)...

    Text Solution

    |

  13. The value of lim(x rarr 0) (int(0)^(x^(2))sec^(2)t dt)/(x sin x) is :

    Text Solution

    |

  14. The value of lim(n rarr oo) (1 + 2^(4) + 3^(4) +…...+n^(4))/(n^(5)) - ...

    Text Solution

    |

  15. lim(x rarr 0) (sin nx[(a-n)nx - tan x])/(x^(2)) = 0, where n is non-ze...

    Text Solution

    |

  16. If lim(h rarr 0) (1 + (a)/(x) + (b)/(x^(2)))^(2x) = e^(2), then the va...

    Text Solution

    |

  17. Let f(x) = (1-tanx)/(4x-pi),x ne (pi)/(4), x in [0, (pi)/(2)], if f(x)...

    Text Solution

    |

  18. Let alpha and beta be the distinct roots of ax^(2) + bx + c = 0, then ...

    Text Solution

    |

  19. lim(x rarr (pi)/(4)) (int(2)^(sec^(2)x) f(t) dt)/(x^(2) - (pi^(2))/(16...

    Text Solution

    |

  20. For x gt 0, lim(x rarr 0) ((sin x)^(1//x) + ((1)/(x))^(sin x)) is :

    Text Solution

    |