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underset( x rarr 0 ) ( "Lim") ((x- 1+ co...

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

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The correct Answer is:
`e^(-1//2)`
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Explore conceptually related problems

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

f(x) is the function such that underset( x rarr 0 ) ("Lim") (f(x))/( x ) = 1 . If underset( x rarr 0 ) ( "Lim") ( x ( 1+ a cos x )-b sinx ) /( (f(x))^(3))= 1 , then find the value of a and b.

The limit underset( x rarr0 ) ( "lim") ( 1- cos x sqrt( cos 2x) )/( x^(2)) is equal to

For x gt 0, underset( x rarr 0) ( "Lim") [ ( sin x)^(1//x) + ((1)/( x))^("sinx ) ] is

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

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

underset( x rarr 0 ) ( "lim")( (1- cos 2x) ( 3 + cos x ))/( x tan 4x) is equal to :

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

underset( x rarr 0 ) ( "lim")((1+sin x )/( 1- sin x ))^("cosec x ") is equal to :

lim_(x rarr0)((x-1+cos x)/(x))^((1)/(x))

MOTION-LIMIT-EXERCISE-3
  1. Evaluate: lim(x->oo) { ((a1)^(1/x)+(a2)^(1/x)+.... +(an)^(1/x))/n}^(n...

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

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

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

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

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

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

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  8. Evaluate lim(x->1)(root13 x- root 7 x)/(root5 x- root3 x)

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  9. lim[x->1] ([sum[k=1]^100x^k]-100])/(x-1)

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  10. lim(x ->oo)x^(2)(sqrt((x+2)/(x))-root(3)((x+3)/(x))) equals

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  11. A circular are of radius 1 subtends an angle of x radians 0 < x < pi/2...

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  12. A circular are of radius 1 subtends an angle of x radians 0 < x < pi/2...

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  13. A circular are of radius 1 subtends an angle of x radians 0 < x < pi/2...

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  14. At the end points A,B of the fixed segment of length L, lines are draw...

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  15. At the endpoint and midpoint of a circular are AB, tangent lines are ...

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  16. lim(x->0) [ ln(1+sin^2x) cot ln^2(1+x)]

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  17. lim(x->oo)(a(2x^3-x^2)+b(x^3+5x^2-1)-c(3x^3+x^2))/(2(5x^4-x)-b x^4+c(4...

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  18. find a&b if lim(x->oo) ((x^2+1)/(x+1)-ax-b)=0

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  19. lim(x rarr oo) (sqrt(x^2-x+1)-a x-b)=0, then a+b=

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  20. lim(x->0)[lim(x->oo)(e x p(xln(1+(a y)/x))-e x p(x In(1+(b y)/x)))/y]

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