Home
Class 12
MATHS
Prove that: underset(xrarrinfty)lim sqrt...

Prove that: `underset(xrarrinfty)lim sqrtx (sqrt(x+3) - sqrtx)= 3/2`

Promotional Banner

Topper's Solved these Questions

  • HIGHER SECONDARY QUESTION 2019

    UNITED BOOK HOUSE|Exercise EXERCISE|40 Videos

  • MODEL QUESTION PAPER SET 10

    UNITED BOOK HOUSE|Exercise EXERCISE|28 Videos

Similar Questions

Explore conceptually related problems

Prove that: underset(xrarrinfty)lim ((x+5)/(x+1))^x = e^4

Prove : underset(xrarroo)"lim"sqrt(x)[sqrt(x+2)-sqrt(x)]=1

Prove that: underset(xrarr0)lim [1+3x]^((x+3)/x = e^9

underset(xto oo)lim(sqrt(x+sqrt(x+sqrtx))-sqrtx)

Prove : underset(xrarr1)"lim"(x^(2)-sqrt(x))/(sqrt(x)-1)=3

Prove : underset(nrarroo)"lim"(sqrt(n+1)-sqrt(n))=0

Prove that : underset(xrarr3)"lim"(x^(2)-9)/(x-3)=6

underset(xto oo)lim(sqrt(x-sqrtx)-sqrtx)

underset(xto 4)lim(sqrt(1+sqrt(2+sqrtx))-sqrt3)/(x-2)

Evaluate : underset(xrarr3)"lim"(sqrt(x-3)+sqrt(x)-sqrt(3))/(sqrt(x^(2)-9)

UNITED BOOK HOUSE-MISCELLANEOUS EXERCISE-EXERCISE
  1. Let X = [(3,2,5),(4,1,3),(0,6,-7):}] express X as sum of two matrics s...

    Text Solution

    |

  2. If [(2,-1),(1,0),(-3,4):}]xxP= [(-1,-8,-10),(1,-2,-5),(9,22,15):}], fi...

    Text Solution

    |

  3. Prove that: underset(xrarrinfty)lim sqrtx (sqrt(x+3) - sqrtx)= 3/2

    Text Solution

    |

  4. Prove that:underset(x rarr0)lim ((x-1+cosx)/(x))^(1/x) = e^(-1/2)

    Text Solution

    |

  5. Prove that: underset(xrarrinfty)lim ((x+5)/(x+1))^x = e^4

    Text Solution

    |

  6. Prove that: underset(xrarrpi/2)lim (1+cosx)^(3secx) = e^3

    Text Solution

    |

  7. Prove that: underset(xrarr0)lim ([1+3x]^((x+3)/x))= e^9

    Text Solution

    |

  8. Evaluate the following limits: underset(x rarr0)lim(xe^x - log(x+1))/(...

    Text Solution

    |

  9. Evaluate the following limits: underset(x rarr0)lim[tan(pi/4+x)]^(1/x)

    Text Solution

    |

  10. Evaluate the following limits: underset(x rarr0)lim(sinx + cos x)^(1/x...

    Text Solution

    |

  11. Evaluate the following limits: underset(x rarr0)limsinlog(1+x)/log(sin...

    Text Solution

    |

  12. It g(x) is the inverse of f(x) and f(X) = (1+x^3)^-1, show that g'(x) ...

    Text Solution

    |

  13. Find the differential coefficients of the folloiwng functions: x^x

    Text Solution

    |

  14. Find form 1st principle the differential coefficients of the folloiwng...

    Text Solution

    |

  15. Find form 1st principle the differential coefficients of the folloiwng...

    Text Solution

    |

  16. Find dy/dx when x^(siny) + y ^(sinx) = 1

    Text Solution

    |

  17. Find dy/dx when x^(logx) + (sinx)^x + 15 x

    Text Solution

    |

  18. Find (d^2y)/(dx^2) when x= e^-t and y = te^-1

    Text Solution

    |

  19. Find (d^2y)/(dx^2) when x= a sin^3t and y = a cos^3 t at t = pi/4

    Text Solution

    |

  20. Find (d^2y)/(dx^2) when x=a(t-sint) and y = a (1+cost) at t = pi/...

    Text Solution

    |