Home
Class 12
MATHS
Letf(x) = underset( n rarr oo)("Lim")und...

Let`f(x) = underset( n rarr oo)("Lim")underset( n=1)overset( n ) ( sum) 3^(n-1) sin^(3) ""(x)/(3^(n)) `and `g(x) = x- 4f(x) `. Evaluate `underset( x rarr 0)("Lim") ( 1+ g(x))^("cotx")`

Text Solution

Verified by Experts

The correct Answer is:
`g(x) = sin x ` and l =e
Promotional Banner

Topper's Solved these Questions

  • LIMIT

    MOTION|Exercise EXERCISE-4|17 Videos

  • LIMIT

    MOTION|Exercise EXERCISE-2(LEVEL-2)|5 Videos

  • INVERSE TRIGONOMETRIC FUNCTIONS

    MOTION|Exercise Exercise -4 Level -II|7 Videos

  • MATRICES

    MOTION|Exercise Exercise - 4 (Level-II)|28 Videos

Similar Questions

Explore conceptually related problems

underset( x rarr 0 ) ("lim") ( cos mx )^(n//x^(2))

Evaluate underset( x rarr0 ) ( "Lim") ( 3 sin x - sin 3x)/( x- sin x )

Find underset( x rarr0 ) ( "Lim") ( tan x - sin x )/( x^(3))

Let f(x) = underset(n rarr oo)("Lim")( 2x^(2n) sin""(1)/(x) +x)/(1+x^(2n)) then find underset( x rarr -oo)("Lim") f(x)

Evaluate: lim_underset(x rarr 0) (sqrt(1+x+x^(2)+x^(3))-1)/(x) .

Let f(x) = underset(n rarr oo)("Lim")( 2x^(2n) sin""(1)/(x) +x)/(1+x^(2n)) then find underset( x rarr 0)("Lim")f(x)

Find underset( x rarr 0 ) ( "Lim") ( e^(sinx) -sin x -1)/( x^(2))

Find underset( x rarr 0 ) ( "Lim") ( e^(sin x) -sin x -1)/( x^(2))

Evaluate : underset( x rarr0 ) ("lim") ( sqrt( ( 1+sin 3x))-1)/(ln ( 1+ tan 2x))

If l = underset( x rarr 0) ("Lim")( x ( 1+ a cos x ) - bsin x ) /( x^(3))= underset( x rarr 0 ) ("Lim") ( 1+a cos x ) /( x^(2))- underset( x rarr 0 ) ("lim")( b sin x )/( x^(3)) , where l in R , then

MOTION-LIMIT-EXERCISE-3
  1. lim(n->oo)sum(r=2)^n((r+1)sinpi/(r+1)-rsinpi/r)

    Text Solution

    |

  2. underset( xrarr oo )("Lim")x^(2) sin(lnsqrt( cos ""( pi)/( x)))

    Text Solution

    |

  3. Letf(x) = underset( n rarr oo)("Lim")underset( n=1)overset( n ) ( sum)...

    Text Solution

    |

  4. Let f(x) = underset(n rarr oo)("Lim")( 2x^(2n) sin""(1)/(x) +x)/(1+x^(...

    Text Solution

    |

  5. Let f(x) = underset(n rarr oo)("Lim")( 2x^(2n) sin""(1)/(x) +x)/(1+x^(...

    Text Solution

    |

  6. Let f(x) = underset(n rarr oo)("Lim")( 2x^(2n) sin""(1)/(x) +x)/(1+x^(...

    Text Solution

    |

  7. Let f(x) = underset(n rarr oo)("Lim")( 2x^(2n) sin""(1)/(x) +x)/(1+x^(...

    Text Solution

    |

  8. Evaluate the limit if exists, lim(x->1)[{ln(1+x)-ln2}{3.4^[x-1]-3x}]...

    Text Solution

    |

  9. lim(x->0)(2 7^x-9^x-3^x+1)/(sqrt(2)-sqrt(1+cosx))

    Text Solution

    |

  10. lim(x->0) tan^(-1) (a/x^2), where a in R

    Text Solution

    |

  11. Plot the graph of the function f(x)=lim(t->0)((2x)/pitan^(- 1)x/(t^2))

    Text Solution

    |

  12. lim(x->oo)((2x^2+3)/(2x^2+5))^(8x^2+3)

    Text Solution

    |

  13. lim(x->oo)((x+c)/(x-c))^x= 4 then find c.

    Text Solution

    |

  14. Evaluate: lim(x->oo) { ((a1)^(1/x)+(a2)^(1/x)+.... +(an)^(1/x))/n}^(n...

    Text Solution

    |

  15. L =lim(x->0)((1)/(ln(1+x))-1/(ln(x+sqrt(1+x^2)))) then find the value ...

    Text Solution

    |

  16. underset( x rarr 0 ) ( "Lim") ((x- 1+ cos x )/( x))^((1)/( x))

    Text Solution

    |

  17. underset( x rarr oo)("Lim")[cos (2pi ((x)/(1+ x ))^(a))]^(x^(2))a in Q

    Text Solution

    |

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

    Text Solution

    |

  19. underset( x rarr 0 ) ("Lim") [ ((1+x)^(1//x))/( e ) ]^(1//x)

    Text Solution

    |

  20. underset( x rarr oo) ("Lim") ((cos h ( pi //x))/(cos( pi//x)))^(x^(2))

    Text Solution

    |