Home
Class 11
MATHS
If a >0,b >0 then (lim)(n->oo)((a-1+b^(...

If `a >0,b >0` then `(lim)_(n->oo)((a-1+b^(1/n))/a)^n=` `b^(1//a)` b. `a^(1/b)` c. `a^b` d. `b^a`

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS

    CENGAGE ENGLISH|Exercise Multiple correct answers type|11 Videos

  • LINEAR INEQUALITIES

    CENGAGE ENGLISH|Exercise All Questions|68 Videos

Similar Questions

Explore conceptually related problems

If agt0, b gt0 than lim_(nrarroo) ((a-1+b^((1)/(n)))/(a))^(n)=

Evaluate: lim_(n->oo)[1/(n a)+1/(n a+1)+1/(n a+2)++1/(n b)]

The value of lim_(ntooo)(e^(n))/((1+(1)/(n))^(n^(2))) is (a) -1 (b) 0 (c) 1 (d) ∞

(lim)_(n->oo)(n !)/((n+1)!+n !) is equal to a. 1 b . 0 c. 2 d. 1/2

lim_(n->oo)(n(2n+1)^2)/((n+2)(n^2+3n-1)) is equal to (a)0 (b) 2 (c) 4 (d) oo

(lim)_(n->oo)(1^2+2^2+3^2++n^2)/(n^3) is equal to a. 1 b . c. 1/3 d. 0

The value of (lim)_(x->oo)(n !)/((n+1)!-(n)!) is a. 1 b . -1 c. 0 d. none of these

The value of (lim)_(n->oo)((n+2)!+(n+1)!)/((n+2)!-(n+1)!) is a. 1 b . -1 c. 0 d. none of these

If the expansion in powers of x of the function 1//[(1-a x)(1-b x)] is a a_0+a_1x+a_2x^2+a_3x^3+ ,t h e na_n i s a. (b^n-a^n)/(b-a) b. (a^n-b^n)/(b-a) c. (b^(n+1)-a^(n+1))/(b-a) d. (a^(n+1)-b^(n+1))/(b-a)

Let aa n db be two real numbers such that a >1,b > 1. If A=(a0 0b) , then (lim)_(nvecoo)A^(-n) is a. unit matrix b. null matrix c. 2l d. none of these

CENGAGE ENGLISH-LIMITS AND DERIVATIVES-All Questions
  1. The value of (lim)(xvec3)((x^3+27)(log)e(x-2))/(x^2-9) is a. 9 b. 1...

    Text Solution

    |

  2. If (lim)(xvec0)(e^(a x)-e^x-x)/(x^2)=b (finite), then a=2,b=0 b. a=0,b...

    Text Solution

    |

  3. If underset(xrarr0)(lim)(x^3)/(sqrt(a+x)(bx-sinx))=1,agt0, then a+b is...

    Text Solution

    |

  4. underset(xrarr0)(lim)[(sin^(-1)x)/(tan^(-1)x)]= (where [.] denotes the...

    Text Solution

    |

  5. The value of lim(x->pi/4) (sqrt(1-sqrt(sin2x)))/(pi-4x) is

    Text Solution

    |

  6. lim(x->0) (sin x /x)

    Text Solution

    |

  7. If f(x)=x((e^(|x|+[x])-2)/(|x|+[x])) then (where [.] represents the gr...

    Text Solution

    |

  8. If A=underset(xrarr0)(lim)(sin^(-1)(sinx))/(cos^(-1)(cosx))and B=under...

    Text Solution

    |

  9. Let f(x)=lim(m->oo){lim(n->oo)cos^(2m)(n !pix)}, where x in Rdot Then...

    Text Solution

    |

  10. lim(x->oo ){(e^x+pi^x)^(1/x)}= where {.} denotes the fractional par...

    Text Solution

    |

  11. Let f(x)=(lim)(xvecoo)(tan^(-1)(tanx))/(1+((log)e x)^n),x!=(2n+1)pi/2 ...

    Text Solution

    |

  12. Assume that underset(thetararr-1)(lim)f(theta) exists and (theta^(2)+t...

    Text Solution

    |

  13. lim(n->oo) ((sqrt(n^2+n)-1)/n)^(2sqrt(n^2+n)-1)

    Text Solution

    |

  14. Let f: RvecR be such that f(a)=1,f^(prime)(a)=2. Then (lim)(xvec0)((...

    Text Solution

    |

  15. lim(x->oo)(1-x+x.e^(1/n))^n

    Text Solution

    |

  16. If f(n)=underset(xto0)lim{(1+"sin"(x)/(2))(1+"sin"(x)/(2^(2)))...(1+"s...

    Text Solution

    |

  17. If a >0,b >0 then (lim)(n->oo)((a-1+b^(1/n))/a)^n= b^(1//a) b. a^...

    Text Solution

    |

  18. (lim)(xvec-pi/2 )[1+(cos x)^(cos x)]^2=

    Text Solution

    |

  19. (lim)(xvec0)("log"(e^x^2+2sqrt(x)))/(t a nsqrt(x)) is equal to 0 b. 1 ...

    Text Solution

    |

  20. If f(x)=(lim)(nvecoo)(cos(x/(sqrt(n))))^n , then the value of (lim)(xv...

    Text Solution

    |