Home
Class 12
MATHS
If L=lim(xto2)((10-x)^(1//3)-2)/(x-2), t...

If `L=lim_(xto2)((10-x)^(1//3)-2)/(x-2)`, then the value of `|1//(4L)|" is "`_________.

Text Solution

Verified by Experts

The correct Answer is:
`(3)`
`underset(xto2)lim((10-x)^(1//3)-2)/(x-2)=underset(hto0)lim((8-h)^(1//3)-2)/(h)" "("Put "x=2+h)`
`=underset(hto0)lim(2(1-(h)/(8))^(1//3)-2)/(h)=2underset(hto0)lim((1+(h)/(8))^(1//3)-1)/(h)`
`=2underset(hto0)lim(1-(1)/(3)(h)/(8)-1)/(h)=-(1)/(12)`
Promotional Banner

Topper's Solved these Questions

  • LIMITS

    CENGAGE|Exercise JEE Main Previous Year|8 Videos

  • LIMITS

    CENGAGE|Exercise JEE Advanced Previous Year|7 Videos

  • LIMITS

    CENGAGE|Exercise Exercise (Matrix)|5 Videos

  • JEE 2019

    CENGAGE|Exercise Chapter 10|9 Videos

  • LINEAR COMBINATION OF VECTORS, DEPENDENT AND INDEPENDENT VECTORS

    CENGAGE|Exercise DPP 1.2|10 Videos

Similar Questions

Explore conceptually related problems

If L=lim_(x rarr2)((10-x)^((1)/(3))-2)/(x-2), then the value of (1)/(4L)| is

If L= lim_(xto2) (root(3)(60+x^(2))-4)/(sin(x-2)) , then the value of 1//L is________.

If L=lim_(xto0) (e^(-x^(2)//2)-cosx)/(x^(3)sinx) , then the value of 1//(3L) is ________.

Evaluate lim_(xto2)(x^(3)-2^(3))/(x-2)

If L=lim_(x rarr oo){x-x^(2)log_(e)(1+(1)/(x))}, then the value of 8L is

If L=lim_(x rarr0)(e^(-((x^(2))/(2)))-cos x)/(x^(3)sin x), then the value of (1)/(3L) is

If l=lim_(xtooo)((x+1)/(x-1))^(x) , the value of {l} and [l] are

State whether the following statements are True of False. If L=lim_(xto0)(sinx-tan x)/(x^(3)), So the value of 2L is 1.

If lim_(xto0)(sin^(-1)x-tan^(-1)x)/(3x^3) is equal to L, then the value of (6L+1) is :

If L=-lim_(ntooo) (2xx3^(2)xx2^(3)xx3^(4)...xx2^(n-1)xx3^(n))^((1)/((n^(2)+1))) , then the value of L^(4) is _____________.

CENGAGE-LIMITS-Exercise (Numerical)
  1. If f(x)={{:(x-1", "xge1),(2x^(2)-2", "xlt1):},g(x)={{:(x+1", ...

    Text Solution

    |

  2. If lim(xtooo) f(x) exists and is finite and nonzero and if lim(xtooo) ...

    Text Solution

    |

  3. If L=lim(xto2)((10-x)^(1//3)-2)/(x-2), then the value of |1//(4L)|" is...

    Text Solution

    |

  4. If lim(xto0) (p sin2x+(1-cos2x))/(x+tanx)=1, then the value of p is.

    Text Solution

    |

  5. The value of lim(xtooo) ((100)/(1-x^(100))-(50)/(1-x^(50))) is .

    Text Solution

    |

  6. If L= lim(xto2) (root(3)(60+x^(2))-4)/(sin(x-2)), then the value of 1/...

    Text Solution

    |

  7. The value of lim(xtooo) ((20^(x)-1)/(19(5^(x))))^(1//x) is .

    Text Solution

    |

  8. The value of lim(ntooo) [root(3)((n+1)^(2))-root(3)((n-1)^(2))] is .

    Text Solution

    |

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

    Text Solution

    |

  10. The value of lim(x to oo ) (log(e)(log(e)x))/(e^(sqrt(x))) is .

    Text Solution

    |

  11. If lim(xto0) (1-sqrt(cos2x).root(3)(cos3x).root(4)(cos4x)...root(n)(co...

    Text Solution

    |

  12. The value of lim(x to oo ) (x-x^(2)log(e)(1+(1)/(x))) is .

    Text Solution

    |

  13. Let S(n)=1+2+3+...+n " and " P(n)=(S(2))/(S(2)-1).(S(3))/(S(3)-1).(S(4...

    Text Solution

    |

  14. If lim(xto1)(asin(x-1)+bcos(x-1)+4)/(x^(2)-1)=-2, then |a+b| is.

    Text Solution

    |

  15. Let lim(xto1) (x^(a)-ax+a-1)/((x-1)^(2))=f(a). Then the value of f(4) ...

    Text Solution

    |

  16. Number of integral values of k for which lim(xto1) sin^(-1)((k)/(log...

    Text Solution

    |

  17. If lim(xto1) (1+ax+bx^(2))^((e)/((x-1)))=e^(3), then the value of bc i...

    Text Solution

    |

  18. Let f''(x) be continuous at x=0 If lim(xto0) (2f(x)-3af(2x)+bf(8x))/...

    Text Solution

    |

  19. If L=lim(xto0) (e^(-x^(2)//2)-cosx)/(x^(3)sinx), then the value of 1//...

    Text Solution

    |

  20. The integer n for which lim(xto0) ((cosx-1)(cosx-e^(x)))/(x^(n)) is a ...

    Text Solution

    |