Home
Class 11
MATHS
If 3-((x^2)/(12))lt=f(x)lt=3+((x^3)/9) f...

If `3-((x^2)/(12))lt=f(x)lt=3+((x^3)/9)` for all `x!=0,` then find the value of `("lim")_(xvec0)f(x)`

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 3-((x^(2))/(12))lef(x)le3+((x^(3))/(9)) in the neighborhood of x=0, then find the value of lim_(xto0) f(x).

Evaluate: ("lim")_(xvec0)(x2^x-x)/(1-cosx)

Evaluate: ("lim")_(xvec0)(tanx-sinx)/(x^3)

If y=f(x^3),z=g(x^5),f^(prime)(x)=tanx ,a n dg^(prime)(x)=secx , then find the value of (lim)_(xvec0)(((dy)/(dz)))/x

Evaluate: ("lim")_(xvec0)(e^x^2-cosx)/(x^2)

Find ("lim")_(xvec0){tan(pi/4+x)}^(1//x)

If f(x) is differentiable and strictly increasing function, then the value of ("lim")_(xvec0)(f(x^2)-f(x))/(f(x)-f(0)) is 1 (b) 0 (c) -1 (d) 2

Evaluate: ("lim")_(xvec0)(1-cosm x)/(1-cosn x)

If f(x)=(lim)_(nvecoo)(cos(x/(sqrt(n))))^n , then the value of (lim)(xvec0)(f(x)-1)/x is 0 b. 1 c. 2 d. 3//2

If f(x)={x/(s in x),x >0 2-x ,xlt=0 and g(x)={x+3,x<1x^2-2x-2,1lt=x<2x-5,xgeq2 Then the value of (lim)_(xvec0)g(f(x)) a. is -2 b. is -3 c. is 1 d. does not exist

CENGAGE ENGLISH-LIMITS AND DERIVATIVES-All Questions
  1. If [dot] denotes the greatest integer function, then find the value of...

    Text Solution

    |

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

    Text Solution

    |

  3. If 3-((x^2)/(12))lt=f(x)lt=3+((x^3)/9) for all x!=0, then find the val...

    Text Solution

    |

  4. If f(x)={x-1,xgeq 1 2x^2-2,x<1,g(x)={x+1,x >0-x^2+1,xlt=0,a n dh(x) ...

    Text Solution

    |

  5. Evaluate the limits using the expansion formula of functions ("lim")(x...

    Text Solution

    |

  6. lim(xrarrinfty),where (2x-3)/xltf(x)lt(2x^2+5x)/x^2,is

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  9. Evaluate the limits using the expansion formula of functions ("lim")(x...

    Text Solution

    |

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

    Text Solution

    |

  11. Evaluate : ("lim")(xvec2)(x^2-5x+6)/(x^2-4)

    Text Solution

    |

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

    Text Solution

    |

  13. Evaluate : ("lim")(xvec1)(2/(1-x^2)+1/(x-1))

    Text Solution

    |

  14. ("lim")(xvec0)((1+5x^2)/(1+3x^2))^1//x^2=

    Text Solution

    |

  15. Evaluate : ("lim")(xto1)(x^2+x(log)e x-(log)e x-1)/((x^2-1)

    Text Solution

    |

  16. If L=("lim")(nvecoo)(2x3^2x2^3x3^4 x2^(n-1)x3^n)^1/((n^(2+1)) , then t...

    Text Solution

    |

  17. Evaluate ("lim")(xvecpi/4)(1-sin2x)/(1+cos4x)

    Text Solution

    |

  18. The value of lim(x->oo)((log)e((log)e x)/(e^(sqrt(x)))i s

    Text Solution

    |

  19. Evaluate : ("lim")(xvecpi/4)(1-cot^3x)/(2-cotx-cot^3x)

    Text Solution

    |

  20. lim(y->0)((x+y)sec(x+y)-xsecx)/y is equal to (a) secx(xtanx+1) (b) x...

    Text Solution

    |