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)

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS

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

    CENGAGE ENGLISH|Exercise All Questions|68 Videos

Similar Questions

Explore conceptually related problems

If f: R->R is defined by f(x)=3x+2 , find f(f(x)) .

Let f(3)=4 and f'(3)=5 . Then lim_(xrarr3) [f(x)] (where [.] denotes the greatest integer function) is

Let f : R rarr R be defined by f(x) = x^(2) - 3x + 4 for all x in R , then f (2) is equal to

If f(x) = (e^([x] + |x|) -3)/([x] + |x|+ 1) , then: (where [.] represents greatest integer function)

If f: R ->R is defined by f(x) = x^2- 3x + 2 , find f(f(x)) .

Let f:(2,4)->(1,3) where f(x) = x-[x/2] (where [.] denotes the greatest integer function).Then f^-1 (x) is

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

If f(x) =2 [x]+ cos x , then f: R ->R is: (where [ ] denotes greatest integer function)

Let f : R->R be given by f(x) = {|x-[x]| , when [x] is odd and |x-[x]-1| , when [x] is even ,where [.] denotes the greatest integer function , then int_-2^4 f(x) dx is equal to (a) (5)/(2) (b) (3)/(2) (c) 5 (d) 3

If f: R to R is defined by f(x)=x-[x]-(1)/(2) for all x in R , where [x] denotes the greatest integer function, then {x in R: f(x)=(1)/(2)} is equal to

CENGAGE ENGLISH-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. Set of all values of x such that underset(nrarroo)(lim)(1)/(1+((4tan^(...

    Text Solution

    |

  10. limxvecoo[x-loge((e^x+e^(-x))/2)]= a)(log)e4 b. 0 c. oo d. (log)e2

    Text Solution

    |

  11. The value of ("lim")(xvec0)(1+sinx-cosx+"log"(1-x))/(x^3)i s 1/2 (b)...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |