Home
Class 11
MATHS
Evaluate the following limit: (lim)(x->p...

Evaluate the following limit: `(lim)_(x->pi/4)(f(x)-f(pi/4))/(x-pi/4)` , where `f(x)=sin2x`

Text Solution

Verified by Experts

`(lim)_(x->pi/4)(f(x)-f(pi/4))/(x-pi/4)`

`(lim)_(x->pi/4)(sin2x-sin(pi/2))/(x-pi/4)`

L'Hopital Rule:

`lim_(x rightarrow b) (f(x))/(g(x))=lim_(x rightarrow b) (f'(x))/(g'(x))`

`(lim)_(x->pi/4)(2cos2x)/(1)=2cos(pi/2)=0`

Promotional Banner

Topper's Solved these Questions

  • INTRODUCTIONS TO 3-D COORDINATE GEOMETRY

    RD SHARMA|Exercise Solved Examples And Exercises|114 Videos

  • LINEAR INEQUATIONS

    RD SHARMA|Exercise Solved Examples And Exercises|163 Videos

Similar Questions

Explore conceptually related problems

Evaluate the following limit: (lim)_(x rarr(pi)/(4))(1-tan x)/(x-(pi)/(4))

Evaluate the following limit: (lim)_(x rarr(pi)/(4))(cos x-s in x)/(((pi)/(4)-x)(cos x+s in x))

Evaluate the following limit: (lim)_(x rarr(pi)/(4))(sqrt(2)-cos x-s in x)/(((pi)/(4)-x)^(2))

Evaluate the following limit: (lim)_(x rarr(pi)/(4))(sqrt(2)-cos x-epsilon x)/((4x-pi)^(2))

The value of lim _(x to pi/4) (pi/4 int_2^(sec^2x)f(x)dx)/(x^2-pi^2/16) is

Let f:(0, pi)->R be a twice differentiable function such that (lim)_(t->x)(f(x)sint-f(x)sinx)/(t-x)=sin^2x for all x in (0, pi) . If f(pi/6)=-pi/(12) , then which of the following statement(s) is (are) TRUE? f(pi/4)=pi/(4sqrt(2)) (b) f(x)<(x^4)/6-x^2 for all x in (0, pi) (c) There exists alpha in (0, pi) such that f^(prime)(alpha)=0 (d) f"(pi/2)+f(pi/2)=0

(2)/(x-f((pi)/(12)))+(3)/(x-f((pi)/(4)))+(4)/(x-f((5 pi)/(12)))=0

which of the following statement is // are true ? (i) f(x) =sin x is increasing in interval [(-pi)/(2),(pi)/(2)] (ii) f(x) = sin x is increasing at all point of the interval [(-pi)/(2),(pi)/(2)] (3) f(x) = sin x is increasing in interval ((-pi)/(2),(pi)/(2)) UU ((3pi)/(2),(5pi)/(2)) (4) f(x)=sin x is increasing at all point of the interval ((-pi)/(2),(pi)/(2)) UU ((3pi)/(2),(5pi)/(2)) (5) f(x) = sin x is increasing in intervals [(-pi)/(2),(pi)/(2)]& [(3pi)/(2),(5pi)/(2)]

" f) "lim_(x rarr pi)(sin x)/(pi-x)=?

If f(x)=0 be a quadratic equation such that f(-pi)=f(pi)=0 and f((pi)/(2))=(-3 pi^(2))/(4), then lim_(x rarr pi)(f(x))/(sin(sin x)) is equal to:

RD SHARMA-LIMITS-All Questions
  1. Evaluate the following limit: (lim)(x->pi)(sqrt(5+cos x)-2)/((pi-x)^2)

    Text Solution

    |

  2. Evaluate the following limit: (lim)(x->a)(sin sqrt(x)-sin sqrt(a))/(x-...

    Text Solution

    |

  3. Evaluate the following limit: (lim)(x->pi/4)(f(x)-f(pi/4))/(x-pi/4) , ...

    Text Solution

    |

  4. Evaluate the following limit: lim(x->1)(1-x^2)/(sinpix)

    Text Solution

    |

  5. Evaluate the following limit: lim(x->pi)(1+cos x)/(tan^2x)

    Text Solution

    |

  6. Evaluate the following limit: (lim)(n->oo)2^(n-1)sin(a/(2^n))

    Text Solution

    |

  7. Evaluate the following limit: lim(x->pi/2)(sin2x)/(cos x)

    Text Solution

    |

  8. Evaluate lim(x->pi/3)(sqrt(1-cos6x))/(sqrt2(pi/3-x))

    Text Solution

    |

  9. Evaluate the following limit: lim(x->pi/4)(1-t a n x)/(x-pi/4)

    Text Solution

    |

  10. Evaluate the following limit: lim(x->pi/3)(sqrt(3)-t a n x)/(pi-3x)

    Text Solution

    |

  11. Evaluate the following limit: lim(x->pi//2)(sqrt(2)-sqrt(1+sin x))/(co...

    Text Solution

    |

  12. Evaluate the following limit: lim(x->pi/4)(sqrt(2)-cos x-sin x)/((pi/4...

    Text Solution

    |

  13. Evaluate the following limit: lim(x->a)(cos x-cos a)/(sqrt(x)-sqrt(a))

    Text Solution

    |

  14. Evaluate the following limit: lim(x->a)(cossqrt(x)-cossqrt(a))/(x-a)

    Text Solution

    |

  15. Evaluate the following limit: lim(x->1)(1+cospix)/((1-x)^2)

    Text Solution

    |

  16. Evaluate lim(x->pi/4)(1-sin2x)/(1+cos4x)

    Text Solution

    |

  17. Evaluate: (lim(n->oo)ncos(pi/(4n))sin(pi/(4n))

    Text Solution

    |

  18. Evaluate the following limit: lim(n->oo)(sin(a/(2^n)))/(sin(b/(2^(n\ )...

    Text Solution

    |

  19. Evaluate the following limit: lim(x->2)(x^2-x-2)/(x^2-2x+"sin"(x-2))

    Text Solution

    |

  20. lim(x->1)(1-x)tan(pix)/2=

    Text Solution

    |