Home
Class 12
MATHS
If f (x) = |{:( sin x , cos x , tan x) ,...

If `f (x) = |{:( sin x , cos x , tan x) , (x^(3) , x^(2) , x) , (2x , 1 , x):}|` , then `Lt_(x to 0) (f(x))/(x^(2))=`

A

3

B

(-1)

C

0

D

1

Text Solution

Verified by Experts

The correct Answer is:
D
Promotional Banner

Topper's Solved these Questions

  • INVERSE TRIGONOMETRIC FUNCTIONS

    HIMALAYA PUBLICATION|Exercise QUESTION BANK|219 Videos

  • LINEAR INEQUALITIES

    HIMALAYA PUBLICATION|Exercise QUESTION BANK|54 Videos

Similar Questions

Explore conceptually related problems

Let f(x) =cos x sin 2x , then :

Lt_(x to 0) (x 2^(x) - x)/(1 - cos x ) =

(sin x + sin 3x )/( cos x + cos 3x )= tan 2x

Let f(x) = {{:(x (sin 1//x + sin (1//x^(2))),,x ne 0),(0,,x = 0):} Then lim_(x rarr oo) f(x) equals :

If f(x) = cos x - cos^(2)x + cos^(3)x + …. to oo int f(x) dx =

lim_(x rarr 0) (x tan 2x - 2x tan x)/((1 - cos 2x)^(2)) is :

If f '(x) = cos (log x) and y = f((2x-3)/(2x+5)) then dy/dx =

If f(x) = |(sin x + sin 2x + sin 3x, sin 2x , sin 3x),(3 + 4 sin x, 3, 4 sin x),(1 + sin x, sin x, 1)| then the value of int_0^(-pi//2) f(x) dx equals :

HIMALAYA PUBLICATION-LIMITS, CONTINUITY AND DIFFERENTIABILITY-QUESTION BANK
  1. The value of lim(x rarr 0) (sqrt(a+x)- sqrt(a-x))/x =

    Text Solution

    |

  2. The value of Lim(xto pi)(sqrt(2+cosx)-1)/((pi-x)^(2)) is

    Text Solution

    |

  3. If f (x) = |{:( sin x , cos x , tan x) , (x^(3) , x^(2) , x) , (2x , 1...

    Text Solution

    |

  4. If f(a)=2,f'(a)=1,g(a)=-3,g'(a)=-1 then Lim(xtoa)(f(a)g(x)-f(x)g(a))/(...

    Text Solution

    |

  5. lim(x rarr 0) (1-ax)^(1/x) =

    Text Solution

    |

  6. Lim(nto oo)(3^(n)+4^(n))^((1)/(n))=

    Text Solution

    |

  7. lim(x rarr oo) (1-4/(x-1))^(3x-1) =

    Text Solution

    |

  8. The value of lim(x rarr 1) (tan^(2)(x-1))/(x^(3)-x^(2)-x+1) =

    Text Solution

    |

  9. lim(theta rarr pi/2) (pi/2- theta)/(cot theta) =

    Text Solution

    |

  10. lim(x rarr 0) (tan x - sin x)/(x^(3)) =

    Text Solution

    |

  11. The value of lim(x to 0)(5^(x)-5^(-x))/(2x)=

    Text Solution

    |

  12. lim(x-1)(tan(x^(2)-1))/(x-1) is equal to

    Text Solution

    |

  13. The value of lim(x rarr oo) (3^(x+1) - 5^(x+1))/(3^(x)-5^(x) is

    Text Solution

    |

  14. If G(x) = -sqrt(25-x^(2)) the lim(x rarr 1) (G(x)-G(1))/(x-1) =

    Text Solution

    |

  15. lim(n rarr oo) ((1)/(1-n^(2)) + (2)/(1-n^(2)) +…...+(n)/(1-n^(2))) is ...

    Text Solution

    |

  16. lim(x rarr oo) ((2 + x)^(40) (4 + x)^(5))/((2-x)^(45)) is :

    Text Solution

    |

  17. lim(x rarr oo) x^(n)/e^(x) = 0 (n is an integer) for

    Text Solution

    |

  18. If f(x) = sqrt((x-sinx)/(x+cos^(2)x)), then lim(x rarr oo) f(x) =

    Text Solution

    |

  19. lim(x rarr 0) {tan (pi/4+x)}^(1/x) =

    Text Solution

    |

  20. The value of lim(x rarr 0) ((1 + 5x^(2))/(1+3x^(2)))^(1//x^(2)) is :

    Text Solution

    |