Home
Class 11
MATHS
If f:R->R is defined by f(x)=[x−3]+|x−4|...

If `f:R->R` is defined by `f(x)=[x−3]+|x−4|` for `x in R`, then `lim_(x->3) f(x)` is equal to (where [.] represents the greatest integer function)

Promotional Banner

Topper's Solved these Questions

  • DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS

    CENGAGE PUBLICATION|Exercise Multiple correct answers type|11 Videos
  • LINEAR INEQUALITIES

    CENGAGE PUBLICATION|Exercise All Questions|68 Videos

Similar Questions

Explore conceptually related problems

Draw a graph of f(x) = sin {x} , where {x} represents the greatest integer function.

Find the range of f(x)=(x-[x])/(1-[x]+x '),w h e r e[] represents the greatest integer function.

f:(2,3)->(0,1) defined by f(x)=x-[x] ,where [dot] represents the greatest integer function.

Find the domain of f(x)=sqrt(([x]-1))+sqrt((4-[x])) (where [ ] represents the greatest integer function).

If f(x)=cos |x|+[|sin x/2|] (where [.] denotes the greatest integer function), then f (x) is

Find the domain of the function f(x)=(1)/([x]^(2)-7[x]-8) , where [.] represents the greatest integer function.

Find the domain and range of f(x)="sin"^(-1)(x-[x]), where [.] represents the greatest integer function.

Suppose that f is an even, periodic function with period 2 , and f(x)=x for all x in the interval [0,1] . The values of [10f(3. 14)] is (where [.] represents the greatest integer function) ______

If f : R rarr R is defined by f(x)=1/(2-cos3x) for each x in R , then the range of f is

Find the number of points where f(x)=[x/3],x in [0, 30], is discontinuous (where [.] represents greatest integer function).

CENGAGE PUBLICATION-LIMITS AND DERIVATIVES-All Questions
  1. (lim)(X-> (-7)([x]^2+15[x]+56)/("sin"(x+7)"sin"(x+8))= (where [.] deno...

    Text Solution

    |

  2. Let L1=(lim)(x^vec4)(x-6)^x and L2=(lim)(x^vec4)(x-6)^4dot Which of t...

    Text Solution

    |

  3. If f:R->R is defined by f(x)=[x−3]+|x−4| for x in R, then lim(x->3) f(...

    Text Solution

    |

  4. If [dot] denotes the greatest integer function, then (lim)(xvec0)x/a...

    Text Solution

    |

  5. underset(xrarr(-1)/(3))(lim)(1)/(x)[(-1)/(x)]= (where [.] denotes the ...

    Text Solution

    |

  6. (lim)(xvecoo)x^2sin((log)esqrt(cospi/x)) a. 0 b. (pi^2)/2 c. (pi^2...

    Text Solution

    |

  7. underset(xrarr0)(lim)(1)/(x^(2))|(1-cos3x,log(e)(1+4x)),(sin^(-1)(x^(x...

    Text Solution

    |

  8. If graph of the function y=f(x) is continuous and passes through point...

    Text Solution

    |

  9. lim(x->oo)[x-loge((e^x+e^(-x))/2)]= a)(log)e4 b. 0 c. oo d. (log)e...

    Text Solution

    |

  10. The value of lim(x->0)(1+sinx-cosx+"log"(1-x))/(x^3) is (a)1/2 ...

    Text Solution

    |

  11. If underset(xrarroo)(lim)((x+c)/(x-c))^(x)=4 then the value of e^(c) i...

    Text Solution

    |

  12. If f(x)=underset(nrarroo)(lim)((x^(2)+ax+1)+x^(2n)(2x^(2)+x+b))/(1+x^(...

    Text Solution

    |

  13. If lim(x->0)[1+x+(f(x))/x]^(1/x)=e^3, then find the value of 1n(lim(x-...

    Text Solution

    |

  14. Let f(x) be the fourth degree polynomial such that f^(prime)(0)-6,f(0)...

    Text Solution

    |

  15. Let f(x) be the fourth degree polynomial such that f^(prime)(0)-6,f(0)...

    Text Solution

    |

  16. (lim)(x->0)((sqrt(1+xsin x)-sqrt(cos2x))/(tan^2(x//2))) is equal to 1/...

    Text Solution

    |

  17. The value of underset(xrarroo)(lim)x^(2)(1-cos.(1)/(x)) is

    Text Solution

    |

  18. lim(x->0) (Cosx -1)/x is equal to

    Text Solution

    |

  19. lim x→(2^+) { x } sin( x−2 ) /( x−2)^2 ...

    Text Solution

    |

  20. The value of lim(x->0)(sqrt(1-cos"x"^2))/(1-cosx) is a.1/2 b. 2 c. s...

    Text Solution

    |