Home
Class 11
MATHS
Assume that underset(thetararr-1)(lim)f(...

Assume that `underset(thetararr-1)(lim)f(theta)` exists and `(theta^(2)+theta-2)/(theta+3)le(f(theta))/(theta^(2))le(theta^(2)+2theta-1)/(theta+3)` holds for certain interval containing the point `theta=-1 " then "underset(thetararr-1)(lim)f(theta)`

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

Assume that lim_(thetararr-1) f(theta) exists and (theta^(2)+theta-2)/(theta+3)le(f(theta))/(theta^(2))le(theta^(2)+2theta-1)/(theta+3) holds for certain interval containing the point theta=-1 " then "lim_(thetararr-1) f(theta)

Prove that : (tan^(2)theta)/(1+tan^(2)theta)+(cot^(2)theta)/(1+cot^(2)theta)=1

Prove that (tan^(2)2theta-tan^(2)theta)/(1-tan^(2)2thetatan^(2)theta)=tan 3 theta tan theta .

(sin^(3) theta-cos^(3) theta)/(sin theta - cos theta)- (cos theta)/sqrt(1+ cot^(2) theta)-2 tan theta cot theta=-1 if

(2 sin theta*cos theta - cos theta)/(1-sin theta+sin^2 theta-cos^2 theta) = cot theta

If theta=pi/(4n) then the value of tanthetatan(2theta)tan(3theta)....tan((2n-1)theta) is

Prove that (tan theta)/(sec theta -1)+ (tan theta)/(sec theta +1) = 2 cosec\ theta

If "tan" 2 theta "tan" theta =1, "then" theta =

(1+sin2theta+cos2theta)/(1+sin2theta-cos2theta)=?

(1+sin 2theta+cos 2theta)/(1+sin2 theta-cos 2 theta) =

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

    |