Home
Class 12
MATHS
For x in (0, pi/2) identify which is gr...

For `x in (0, pi/2)` identify which is greater `(2 sin x + tan x ) ` or `(3x)`. Hence find `{:(" "lim),(x rarr0):} [(3x)/(2sinx+tanx)]` where `[**]` denote the greatest integer function.

Text Solution

Verified by Experts

The correct Answer is:
`2 sinx+tan x gt 3x`, limit `=0`
Promotional Banner

Topper's Solved these Questions

  • MONOTONOCITY

    MOTION|Exercise Exercise - 3 ( Subjective ) COMPREHENSION|4 Videos

  • MONOTONOCITY

    MOTION|Exercise Exercise - 4 ( Level-I ) Previous Year|4 Videos

  • MONOTONOCITY

    MOTION|Exercise Exercise - 2 (Level-II) ( Multiple Correct ) MIXED PROBLEMS|5 Videos

  • METHOD OF DIFFERENTIATION

    MOTION|Exercise EXERCISE - 4 LEVEL -II|5 Videos

  • PARABOLA

    MOTION|Exercise EXERCISE - IV|33 Videos

Similar Questions

Explore conceptually related problems

lim_(x rarr0^(+))[(3x)/(2sin x+tan x)]

lim_(x rarr0)[(99tan x sin x)/(x^(2))] = Where [.] denotes the greatest integer function

lim_(x rarr0)(x)/(sin2x)

lim_(x rarr0)(x)/(sin2x)

The value of lim_(x rarr0)[(x^(2))/(sin x tan x)] (Wherer [*] denotes greatest integer function) is

lim_(x rarr0)(x[x])/(sin|x|) , where [.] denote greater integer function

lim_(x rarr0)(sin2x+3x)/(2x+tan3x)

The value of lim_(x rarr0)[(sin x)/(x)] is (where [.] denotes greatest integer function)

Evaluate: [(lim)_(x rarr0)(tan^(-1)x)/(x)], where [ lrepresent the greatest integer function

Evaluate: lim_(x rarr0)(sin x)/(x), where [.] represents the greatest integer function.

MOTION-MONOTONOCITY-Exercise - 3 ( Subjective )
  1. Find the intervals of monotonocity for the following functions & repre...

    Text Solution

    |

  2. Let f(x)={:{(x^(2),x ge 0),(ax, x lt 0):}. Find real values of a such...

    Text Solution

    |

  3. If f(x) = x^(3) + (a – 1) x^(2) + 2x + 1 is strictly monotonically in...

    Text Solution

    |

  4. Find the values ' a ' for which the function f(x)=(a+2)x^3-3a x^2+9a x...

    Text Solution

    |

  5. Find the greatest & least value of f(x)=sin^(-1).(x)/(sqrt(x^(2)+1)...

    Text Solution

    |

  6. Using monotonicity prove that x lt - ln (1-x) lt x (1-x)^(-1) for ...

    Text Solution

    |

  7. Using monotonicity prove that (x)/(1-x^(2)) lt tan^(-1)x lt x for...

    Text Solution

    |

  8. Prove that tan^2x+6lns e c x+2cosx+4>6secx for x\ in ((3pi)/2,\...

    Text Solution

    |

  9. Verify Rolles theorem for the function f(x)=log{(x^2+a b)/(x(a+b))}...

    Text Solution

    |

  10. Using Rolle's theorem prove that the equation 3x^2 + px - 1 = 0 has th...

    Text Solution

    |

  11. f(x) and g(x) are differentiable functions for 0 le x le 2 such that ...

    Text Solution

    |

  12. Show that the lagranges mean value theorem is not applicable to the...

    Text Solution

    |

  13. If a, b are two real numbers with a lt b show that a real number 'c' ...

    Text Solution

    |

  14. Using LMVT prove that : (a) tan x gt x in (0, pi/2), (b) sin x l...

    Text Solution

    |

  15. Construct the graph of the function f(x)=-|(x^(2)-9)/(x+3)-x+(2)/(x-...

    Text Solution

    |

  16. Show that exactly two real values of x satisfy the equation x^2= xsinx...

    Text Solution

    |

  17. If g(x) is monotonically increasing and f(x) is monotonically decreasi...

    Text Solution

    |

  18. For x in (0, pi/2) identify which is greater (2 sin x + tan x ) or ...

    Text Solution

    |

  19. Using monotonocity find range of the function f(x)=sqrt(x-1)+sqrt(6...

    Text Solution

    |

  20. Let f(x) = x^(3) - x^(2) + x + 1 and g(x) = {{:(max f(t)",", 0 le t le...

    Text Solution

    |