Home
Class 11
MATHS
The integer n for which lim(x rarr0)((co...

The integer n for which `lim_(x rarr0)((cos x-1)(cosx-e^x))/x^n` is a finite non-zero number is :

Promotional Banner

Topper's Solved these Questions

  • DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS

    CENGAGE PUBLICATION|Exercise Multiple correct answers type|11 Videos

  • LINEAR INEQUALITIES

    CENGAGE PUBLICATION|Exercise All Questions|68 Videos

Similar Questions

Explore conceptually related problems

Find the integral value of n for which lim_(x->0)(cos^2x-cosx-e^xcosx+e^x-(x^3)/2)/(x^n) is a finite nonzero number

lim_(x rarr 0) (sin(pi sin^2 x))/x^2=

lim_(x rarr 0) ((1+tan x)/(1-tan x))^(1/x) is

lim_(x to 0) (cos5x-cos7x)/(cosx-cos5x)

Evaluate: lim_(x rarr 0)(e^(4x)-1)/(x)

The value of lim_(x rarr 0) (e^(x2)-1)/(x) is

The value of lim_(x rarr 0)(a^(2x)-1)/(2x) is

Evaluate: lim_(x rarr 0) (e^(sinx)-1)/(x)

Evaluate: lim_(x rarr 0)(e^(13x)-e^(7x))/(x)

Show that , lim_(x rarr 0)(3^(x)+3^(-x)-2)/(x^(2)

CENGAGE PUBLICATION-LIMITS AND DERIVATIVES-All Questions
  1. If underset(xto1)lim(asin(x-1)+bcos(x-1)+4)/(x^(2)-1)=-2, then |a+b| i...

    Text Solution

    |

  2. Evaluate the limit lim(x->0)(sin3x)/x

    Text Solution

    |

  3. The integer n for which lim(x rarr0)((cos x-1)(cosx-e^x))/x^n is a fin...

    Text Solution

    |

  4. Evaluate the limit: ("lim")(nrarroo)((1^2-2^2+3^2-4^2+5^2+ nt e r m s)...

    Text Solution

    |

  5. Let ("lim")(xvec1)(x^a-a x+a-1)/((x-1)^2)=f(a)dot Then the value of f(...

    Text Solution

    |

  6. Evaluate the limit: lim(x->a)(sqrt(3x-a)-sqrt(x+a))/(x-a)

    Text Solution

    |

  7. f(x)=(3x^2+a x+a+1)/(x^2+x-2) and lim(x->-2)f(x) exists. Then th...

    Text Solution

    |

  8. Evaluate the limit: ("lim")(x->oo)[sqrt(a^2x^2+a x+1)-sqrt(a^2x^2+1)]

    Text Solution

    |

  9. lim(x->0)(1-sqrt(cos2x)*root(3)(cos3x).....root(n)(cosnx))/x^2 has ...

    Text Solution

    |

  10. Evaluate the limit: lim(x->1)(sum (k=1) ^100 x^k-100)/(x-1)

    Text Solution

    |

  11. Let Sn=1+2+3++n and Pn=(S2)/(S2-1)*(S3)/(S3-1)*(S4)/(S4-1)* . . . *...

    Text Solution

    |

  12. If a(1)=1 and a(n+1)=(4+3a(n))/(3+2a(n)),nge1"and if" lim(ntooo) a(n)=...

    Text Solution

    |

  13. If L=lim(x->oo){x-x^2(log)e(1+1/x)}, then the value of 8L is

    Text Solution

    |

  14. Evaluate the limit: ("lim")(nrarroo)cos(pisqrt(n^2+n))when n is an in...

    Text Solution

    |

  15. Evaluate: lim(x->a)(sqrt(a+2x)-sqrt(3x))/(sqrt(3a+x)-2sqrt(x)),(a!=0)...

    Text Solution

    |

  16. Evaluate the limit: lim(x->0)(sqrt(2)-sqrt(1+cosx))/(sin^2x)

    Text Solution

    |

  17. Let f ''(x) be continuous at x=0 If lim(xto0) (2f(x)-3af(2x)+bf(8x))...

    Text Solution

    |

  18. Evaluate the limit: ("lim")(h -> 0)[1/(h(8+h)^(1/3))-1/(2h)]

    Text Solution

    |

  19. Evaluate: lim(x->0)(e-(1+x)^(1/x))/x

    Text Solution

    |

  20. Using lim(theta -> 0) (sintheta/theta)=1 prove that the area of circ...

    Text Solution

    |