Home
Class 12
MATHS
Prove the following inequalities : tan ...

Prove the following inequalities :
`tan x gt x + x^(3)//3 "if " (0 lt x lt pi//2)`

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • APPLICATION OF DIFFERENTIAL CALCULUS TO INVESTIGATION OF FUNCTIONS

    IA MARON|Exercise MAXIMA AND MINIMA OF FUNCTION|13 Videos

  • APPLICATION OF DIFFERENTIAL CALCULUS TO INVESTIGATION OF FUNCTIONS

    IA MARON|Exercise FINDING THE GREATEST AND THE LEAST VALUES OF A FUNCTION|11 Videos

  • APPLICATION OF DIFFERENTIAL CALCULUS TO INVESTIGATION OF FUNCTIONS

    IA MARON|Exercise APPLICATION OF TAYLOR.S FORMULA TO EVALUATION OF LIMITS|6 Videos

  • APPLICATIONS OF THE DEFINITE INTEGRAL

    IA MARON|Exercise Computing Static Moments and Moments of Inertia. Determining Coordinates of the Centre of Gravity|15 Videos

Similar Questions

Explore conceptually related problems

Prove the inequalities tan x gt x + x^(3) //3 " at" 0 lt x lt pi//2

Solve the following inequalities: (3x+4)/(x^(2)-3x+5)lt0

Solve the following equations : 2tan^(-1) (sin x) = tan^(-1) (2sec x ,) 0 lt x lt pi/2

Solve the inequality: tan x lt 2

Prove the inequalities x-x^(2) lt In (1+x) "at" x gt 0

Prove that tan x gt x + (x^(3))/(3) for all x in (0, pi/2) .

Prove the inequalities 1 +1/2 x - (x^(2))/8 lt sqrt(1+x) lt 1 +1/2 x at 0 lt x lt oo

Solve the inequation : 0lt x/3 lt1

Solve the following inequations: (i) 3x-6lt0 (ii) -3x+9le0 (iii) 7x+5gt33 (iv) 5x-15ge0 .

IA MARON-APPLICATION OF DIFFERENTIAL CALCULUS TO INVESTIGATION OF FUNCTIONS-TESTING A FUNCTION FOR MONOTONICITY
  1. Find the intervals of monotonicity of the following f(x)=2x^2-"ln"|...

    Text Solution

    |

  2. Determine the intervals of monotonicity for the following functions : ...

    Text Solution

    |

  3. Determine the intervals of monotonicity for the following functions : ...

    Text Solution

    |

  4. Determine the intervals of monotonicity for the following functions : ...

    Text Solution

    |

  5. Determine the intervals of monotonicity for the following functions : ...

    Text Solution

    |

  6. Determine the intervals of monotonicity for the following functions : ...

    Text Solution

    |

  7. Find the intervals of decreases and increases for the following funct...

    Text Solution

    |

  8. Prove that the function y = x^(5) +2x^(3)+x increases everywhere and t...

    Text Solution

    |

  9. Determine the intervals of increase and decrease for the following fu...

    Text Solution

    |

  10. Determine the intervals of increase and decrease for the following fu...

    Text Solution

    |

  11. Determine the intervals of increase and decrease for the following fu...

    Text Solution

    |

  12. Determine the intervals of increase and decrease for the following fu...

    Text Solution

    |

  13. Determine the intervals of increase and decrease for the following fu...

    Text Solution

    |

  14. Determine the intervals of increase and decrease for the following fu...

    Text Solution

    |

  15. Prove the following inequalities : tan x gt x + x^(3)//3 "if " (0 lt ...

    Text Solution

    |

  16. Prove the following inequalities : e^(x) ge 1+ x for all the values ...

    Text Solution

    |

  17. Prove the following inequalities : e^(x) gt e^(-x) at x gt 1 .

    Text Solution

    |

  18. At what values of the coefficient a does the function f(x)=a^(3)-ax in...

    Text Solution

    |

  19. Find the values of b for which the function f(x)=sinx-b x+c is a decre...

    Text Solution

    |