Home
Class 11
MATHS
Suppose that f is a function such that 2...

Suppose that `f` is a function such that `2x^2lt=f(x)lt=x(x^2+1)` for all `x` that are near to 1 but not equal to 1. Show that this fact contains enough information for us to find `("lim")_(x->1)f(x)dot` Also, find this limit.

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

If f: R->R is an odd function such that f(1+x)=1+f(x) and x^2f(1/x)=f(x),x!=0 then find f(x)dot

Let f(x)={(log(1+x)^(1+x)-x)/(x^2)}dot Then find the value of f(0) so that the function f is continuous at x=0.

Find the domain of f(x)=sin^(-1)((x^2)/2)dot

If f(x)= int e^(x)(x-1)(x-2)dx , then show that f(x) is a decreasing function 1 lt x lt 2 .

If the function f:[1, infty) rarr [1, infty) is defined by f(x)=2^(x(x-1)) , then find f^(-1)(x)

The function f:R→R satisfies f(x^2 ).f ′′ (x)=f ′ (x).f ′ (x^2 ) for all real x. Given that f(1)=1 and compute the value of f ′ (1)+f ′′ (1) .

If f(x)=3x^2-x+1 , then find f(-1)

Find all the points of discontinuity of the function f defined by {{:(x+2," if "x lt 1),(0," if "x=1),(x-2," if "x gt 1):} .

A function f(x) is defined in a lt x lt b and a lt x_(1) lt x_(2) lt b , then f(x) is strictly monotonic decreasing in a le x le b when-

Find f'(x)" if "f(x)= (sin x)^(sin x) for all 0 lt x lt pi .

CENGAGE PUBLICATION-LIMITS AND DERIVATIVES-All Questions
  1. Evaluate underset(ntooo)lim(1)/(1+n^(2))+(2)/(2+n^(2))+...+(n)/(n+n^(2...

    Text Solution

    |

  2. If L=lim(x->2) ((10-x)^(1/3) -2)/(x-2), then the value of |1/(4L)| ...

    Text Solution

    |

  3. Suppose that f is a function such that 2x^2lt=f(x)lt=x(x^2+1) for all ...

    Text Solution

    |

  4. If L=lim(xto0) (e^(-x^(2)//2)-cosx)/(x^(3)sinx), then find the value o...

    Text Solution

    |

  5. If [dot] denotes the greatest integer function, then find the value of...

    Text Solution

    |

  6. If lim(x->oo) f(x) exists and is finite and nonzero and if lim(x->oo)...

    Text Solution

    |

  7. If 3-((x^(2))/(12))lef(x)le3+((x^(3))/(9)) in the neighborhood of x=0,...

    Text Solution

    |

  8. If f(x)={{:(x-1", "xge1),(2x^(2)-2", "xlt1):},g(x)={{:(x+1", "xg...

    Text Solution

    |

  9. Evaluate underset(xto0)lim{(sinx-x+(x^(3))/(6))/(x^(5))}.

    Text Solution

    |

  10. underset(xtooo)limf(x)," where "(2x-3)/(x)ltf(x)lt(2x^(2)+5x)/(x^(2))A...

    Text Solution

    |

  11. Evaluate underset(xto0)lim(sinx+log(1-x))/(x^(2)).

    Text Solution

    |

  12. If underset(xto0)lim[1+x+(f(x))/(x)]^(1//x)=e^(3), then the value of l...

    Text Solution

    |

  13. Evaluate the limits using the expansion formula of functions lim(x->0)...

    Text Solution

    |

  14. The value of ("lim")(n->oo)[(n+1)^2 3-(n-1)^2 3] is

    Text Solution

    |

  15. Evaluate : lim(x->2)(x^2-5x+6)/(x^2-4)

    Text Solution

    |

  16. If: ("lim")(xrarr1)(1+a x+b x^2)^(c/((x-1)))=e^3, then Find the condit...

    Text Solution

    |

  17. Evaluate : lim(x->1)(2/(1-x^2)+1/(x-1))

    Text Solution

    |

  18. lim(x->0)((1+5x^2)/(1+3x^2))^(1//x^2)=

    Text Solution

    |

  19. Evaluate : lim(x->1)(x^2+x(log)e x-(log)e x-1)/((x^2-1)

    Text Solution

    |

  20. If L= lim(ntooo) (2xx3^(2)xx2^(3)xx3^(4)...xx2^(n-1)xx3^(n))^((1)/((n^...

    Text Solution

    |