Limits — Page 1 — Tinkutara Math Forum

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n ∈ N (Un): { ((U_0 =lim _(n→∞) V_n )),((U_(n+1) =(1/2)(U_n +2^(−n) ))) :} (V_n ): { ((V_(n+1) =(1+((n+1)/n^2 ))V_n )),((V_0 =1)) :} U_0 =? lim_∞ U_n =?

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Question 229201

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calculer la limite suivante lim_(x→0) ((1/k))!×Π_(k=0) ^(n−1) cos (((E(kx))/(k!)))

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Q. lim lim_(x→a y→b) A_(m,n) =L Suppose a double sequence A_(m,n) converges to L. According to the Moore-Osgood Theorem the order of limits can be interchanged if at least one direction converges uniformly. I find this counterintuitve I don′t understand why uniform convergence in just one direction is sufficient to guarantee the validity of switching the limits. It would be much easier to accept if uniform convergence were required in both directions.

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lim_(x→0) ((!x−1)/( (√(x−1))−1))=?

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Question 227067

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Σ_(n∈N∪{0}) tan^(−1) ((1/(n^2 +3n + 2)) )=? ■

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lim_(n→+∞) (((sin (1/n))/(n+(1/1))) + ((sin (2/n))/(n+(1/2))) + ... + ((sin (n/n))/(n+(1/n))))=?

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lim_(x→0) (lim_(n→∞) (cos (x/2) cos (x/2^2 ) ... cos (x/2^n ))) = ?

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a+b+c = x lim_(x→0) ((a^3 +b^3 +c^3 )/(abc)) =?

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lim_(x→0) (((sin x)/x))^((x−3sin x)/x) .?

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P= Π_(k=1) ^∞ (1/( (√(1+(1/k))) (1−(1/(2k))))) =?

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lim_(x→1) ((x(x+(1/x))^5 −32 )/(x−1))

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Prove that: ∫_( 0) ^( (π/2)) tan^(− 1) (r sin θ) dθ = 2𝛘_2 ((((√(1 + r^2 )) − 1)/r))

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if lim_(x→+∞) x−f(x)=+∞ and lim_(x→+∞) x+f(x)=+∞ can we determine lim_(x→+∞) ((x−f(x))/(x+f(x)))

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lim_(x→0) ((1−(√(cos(x))))/( x−xcos((√x))))

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S=Σ_(n=1) ^∞ (−1)^(n−1) (H_n /n^2 ) = ? note: H_n =1+(1/2) +(1/3) +...+(1/n)

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lim_(x→0) ((tan(x^2 +4x))/(sin(9x^2 +x))) No L′ho^ pital′s rule allowed!

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lim_(x→3) (√(x−3))=? 1) 0 2) 3 3) Does not exist 4) Undefined

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lim_(x→2) ((4−2^x )/(x−2))

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lim_(x→2) ((4−x^2 )/(x−2))

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Question 221260

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Question 221047

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Question 221034

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Lim_(x→0) {((xe^x −log(1+x))/x^2 )}

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α ∈ R lim_(x→1) (((1 − x)^α )/(^3 (√(1 − x^4 )))) ∈(0,∞)

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Question 220811

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L= lim _( n→∞) (Σ_(k=1) ^n (k/(n^2 +k^2 ))).(∫^( 1) _( 0) e^(−x^2 ) dx)^(−1) .(Σ_(m=0) ^∞ (((−1)^m )/((2m+1)3^m )))

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lim_(n→∞) tan[(π/4)+(1/n)]^n =?

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lim_(n→∞) n((1/(1+n)) +(1/(2+n)) +...+(1/(2n)) −ln(2))=?

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Question 219731

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Question 219365

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Question 219223

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Prove; lim_(x→0) ((x − sin x)/x^3 ) = (1/6)

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Question 218543

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lim _(n→∞) (1/n) ( (((2n)!)/(n!)) )^(1/n) = ?

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Given a_(n+1) = a_n + a_(n+2) where a_3 = 4 and a_5 = 6 find a_n .

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Question 216953

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Question 216952

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Evaluate 5^2 Σ_(n=1) ^∞ (1/2)(Σ_(m=2) ^∞ (2/(m^2 +2m)))^(n−1)

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Question 216925

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lim_(x→+∞) ((√(x+(√(x+(√(x+(√x)))))))−(√x))

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Find ∫_(−1) ^1 ln∣Γ((1/2)+it)∣dt

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prove that : Σ_(n=1) ^∞ (( cos( n ))/n) ( 1+(1/( (√2))) + (1/( (√3))) + ...+(1/( (√n))) ) is convergent.

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lim_(x→0) ((sin^2 2x)/( ((cos x))^(1/3) −((cos x))^(1/4) )) =?

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lim_(x→0) ((1−cos x (√(cos 2x)))/x^2 ) =?

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lim_(Δx→cos(π/2)) ((sin^3 (Δx+x)−sin^3 x)/(2^(−1) ∙Δx))=?

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lim_(x→0) ((cos 2x−cos 6x)/(1−cos 3x cos 5x)) =?

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lim_(x→∞) (((√((x+1)^3 ))−(√((x−1)^3 )))/( (√x))) =?

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abc = 8 , lim_(x→0) (((a^x +b^x +c^x )/3))^(3/x) .