Home
Class 12
MATHS
Evaluate lim(xtooo) (sqrt(25x^(2)-3x)+5x...

Evaluate `lim_(xtooo) (sqrt(25x^(2)-3x)+5x).`

Text Solution

Verified by Experts

We have
`underset(xtooo)lim(sqrt(25x^(2)-3x)+5x)" "(oo-oo"form")`
`=underset(ytooo)lim(sqrt(25y^(2)+3y)-5y),"where "y=-x`
`=underset(ytooo)lim(25y^(2)+3y-25y^(2))/(sqrt(25y^(2)+3y)+5y)`
`=underset(ytooo)lim(3y)/(sqrt(25y^(2)+3y)+5y)`
`=underset(ytooo)lim(3)/(sqrt(25+(3)/(y))+5)=(3)/(5+5)=(3)/(10)`
Promotional Banner

Topper's Solved these Questions

  • LIMITS

    CENGAGE|Exercise Exercise 2.1|10 Videos

  • LIMITS

    CENGAGE|Exercise Exercise 2.2|7 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

Evaluate: lim_(x rarr oo)(sqrt(25x^(2)-3x)+5x)

Evaluate :lim_(x rarr oo)(sqrt(25x^(2)-3x)+5x)

Evaluate lim_(xtooo) (sqrt(x^(2)+1)-root(3)(x^3+1))/(root(4)(x^(4)+1)-root(5)(x^(4)+1))

lim_(xtooo)[x-sqrt(x^(2)+x]]

Evaluate lim_(xtooo) (1+(2)/(x))^(x).

Evaluate: lim_(x rarr 5) sqrt(25-x^(2)) .

Evaluate lim_(xtooo)(1+2/x)^(x)

Evaluate lim_(xtooo)(x^(2)+5)/(x^(2)+4x+3)

Evaluate lim_(xtooo) (log_(e)x)/(x)

Evaluate lim_(xtooo) ((7x^(2)+1)/(5x^(2)-1))^((x^(5))/(1-x^(3))).

CENGAGE-LIMITS-Question Bank
  1. Evaluate lim(xtooo) (sqrt(25x^(2)-3x)+5x).

    Text Solution

    |

  2. If Lim(x rarr 0) (1-cosx)/(e^(ax)-bx-1) exist and is equal to 1, then ...

    Text Solution

    |

  3. If graph of a function f(x) is shown in the adjacent figure, then Lim(...

    Text Solution

    |

  4. If beta(1)+beta(2)+beta(3)+....+beta(n) = p and Lim(x rarrp)((3-3tan(p...

    Text Solution

    |

  5. Let f(x) be a function continuous for all x except at x =0 such that f...

    Text Solution

    |

  6. Let f(x) =(sec x)^(cosecx) + (cot x)^(sin x). Then the value of Lim(x ...

    Text Solution

    |

  7. Lim(z rarr 0){{max((sin^(-1)x + cos^(-1)x)^(2), min(x^(2)+4x+7))}. (si...

    Text Solution

    |

  8. ((8e^(a))/e)lim(n rarr oo) ((n/(n+1))^(a) + sin (1/n))^(n))where a in ...

    Text Solution

    |

  9. If the value of lim(x rarr oo) (root(3)(x^(3)+x^(2)-root(3)(x^(3)-x^(2...

    Text Solution

    |

  10. Let f(x) be a polynomial satisfying lim(x rarr oo) (x^(2)f(x))/(2x^(5)...

    Text Solution

    |

  11. Let L(1) = Lim(x rarr 0)(cos(pix)(e^(lambda x)-1)/(pi sin x) and L(2) ...

    Text Solution

    |

  12. If Lim(c rarr 0) (asinc+btanc)/c^(3) = 3/2, find the value of |a+2b|.

    Text Solution

    |

  13. Lim(n rarr oo) (1-1/2^(2))(1-1/3^(2))(1-1/4^(2))…(1-1/n^(2)) equals

    Text Solution

    |

  14. The value of Lim(x rarr 0)(sum(k =1)^(2016){(sinx)/x+2015k})/2016 is [...

    Text Solution

    |

  15. Lim(x rarr oo) (30+4sqrtx+7root(3)(x))/(2+sqrt(4x-7)+root(3)(6x-2) )eq...

    Text Solution

    |

  16. If Lim(x rarr0) ((a sin x + b tan x)/x^(3))= 3/2 then |a+2b| is equal ...

    Text Solution

    |

  17. lim(x rarr 0)(1/(1+n^(2))+2/(1+n^(2))+3/(1+n^(2))+....+n/(1+n^(2))) is...

    Text Solution

    |

  18. Find the value of lim(n rarr oo)sum(k=1)^(n)(k^(2)+k-1)/((k+1)!) .

    Text Solution

    |

  19. If Lim(x rarr 0)(1-cos(1-cos(1-cosx)))/x^(a) is finite then teh maximu...

    Text Solution

    |

  20. The value of Lim(x rarr 0)((tanx)^(1/x)+(1+sinx)^(x)) where x gt0 is e...

    Text Solution

    |

  21. Let f(x) be a differentiable function satisfying f(x+y) = f(x)+f(y) A...

    Text Solution

    |