Home
Class 12
MATHS
m,n in I^(+), then lim(x to 0) ("sin"x^...

`m,n in I^(+)`, then `lim_(x to 0) ("sin"x^(n))/(("sin"x)^(m))` equals

A

1, if `n lt m`

B

0, if n = m

C

`(n)/(m)`

D

0, if `n gt m`

Text Solution

Verified by Experts

The correct Answer is:
D
Promotional Banner

Topper's Solved these Questions

  • LIMITS AND DERIVATIVES

    AAKASH INSTITUTE|Exercise Section - C|6 Videos

  • LIMITS AND DERIVATIVES

    AAKASH INSTITUTE|Exercise Section - D|6 Videos

  • LIMITS AND DERIVATIVES

    AAKASH INSTITUTE|Exercise SECTION - A|50 Videos

  • INVERSE TRIGONOMETRIC FUNCTIONS

    AAKASH INSTITUTE|Exercise ASSIGNMENT (SECTION - J)(ANKASH CHALLENGERS QUESTIONS)|4 Videos

  • MATHEMATICAL REASONING

    AAKASH INSTITUTE|Exercise Assignment (SECTION-D) (Assertion-Reason Type Questions)|15 Videos

Similar Questions

Explore conceptually related problems

m,n,in1^(+), then lim_(x rarr0)(sin x^(n))/((sin x)^(m)) equals

lim_(x to a) (x^(m)-a^(m))/(x^(n)-a^(n)) is equal to

lim_(x rarr0)[(sin x sin^(-1)x-x^(2))/(x^(6))] equals

lim_(x rarr0)(log(sin7x+cos7x))/(sin3x) equals.

Find lim_( x to 0) (sin x^(n))/((sin x)^(m)) " where" , m , n in Z^(+) equal

If m,n in N,lim_(x rarr0)(sin x^(m))/((sin x)^(m)) is 1, if n=m(b)0, if n>m oo, if n

If m, n in N , then int_(0)^(pi//2)((sin^(m)x)^(1/n))/((sin^(m)x)^(1/n)+(cos^(m)x)^(1/n))dx is equal to

(2) lim_(n rarr0) (n!sin x)/(n)

AAKASH INSTITUTE-LIMITS AND DERIVATIVES -Section - B
  1. lim(x to 0) (2^(x) - 1)/(sqrt(1 + x) - 1) =

    Text Solution

    |

  2. The value of lim(x to 0) (log (5 + x) - log (5 - x))/(x) equals

    Text Solution

    |

  3. m,n in I^(+), then lim(x to 0) ("sin"x^(n))/(("sin"x)^(m)) equals

    Text Solution

    |

  4. The value of lim(x to (pi)/(4)) ("sin" x - cos x)/((x - (pi)/(4))) eq...

    Text Solution

    |

  5. The value of lim(x to 0) ("sin" (pi cos^(2) x))/(x^(2)) equals

    Text Solution

    |

  6. The value of lim(n to oo) (2n^(2) - 3n + 1)/(5n^(2) + 4n + 2) equals

    Text Solution

    |

  7. The value of lim(theta to (pi)/(2)) (sec theta - tan theta) equals

    Text Solution

    |

  8. The value of lim(x to oo) (sqrt(x^(2) + x + 1) - sqrt(x^(2) - x + 1)) ...

    Text Solution

    |

  9. The value of lim(x to 0) ((1)/(x^(2)) - cot x) equals

    Text Solution

    |

  10. The value of lim(h to 0) {(1)/(h(8 + h)^(1//3)) - (1)/(2h)} equals

    Text Solution

    |

  11. The value of lim(x to oo) {sqrt(x+ sqrt(x + sqrt(x))) - sqrt(x)} equa...

    Text Solution

    |

  12. lim(x to 2) (([x]^(3))/(3) - [(x)/(3)]^(-3)) is where [x] represents t...

    Text Solution

    |

  13. underset(x to 2)(Lt) {[x - 2] + [2 - x] - x} = where [.] represents gr...

    Text Solution

    |

  14. If {x} denotes the fractional part of x, then lim(x to 0) ({x})/(tan ...

    Text Solution

    |

  15. The least integer n for which lim(x to 0) ((cos x - 1) (cos x - e^(x))...

    Text Solution

    |

  16. Let alpha and beta be the distinct roots of ax^(2) + bx + c = 0 then u...

    Text Solution

    |

  17. underset(x to 0)(Lt) (sqrt(1 - cos 2 x))/(sqrt(2)x) =

    Text Solution

    |

  18. The value of lim(x to 0) ("sin" alpha X - "sin" beta x)/(e^(alphax) -...

    Text Solution

    |

  19. The value of lim(x + (pi)/(2)) ({1 - tan (x)/(2)}{1-"sin"x})/({1 + ta...

    Text Solution

    |

  20. The value of lim(x to oo) ((4^(x) - 1)^(3))/("sin"(x)/(4) log (1 + (x...

    Text Solution

    |