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LimitsQuestion and Answers: Page 2
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Question and Answers Forum |
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LimitsQuestion and Answers: Page 2 |
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| lim_(n→∞) Π_(k=1) ^n ((k^2 +1)/( (√(k^2 +4))))=? |
| determinant () |
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| lim_(n→∞) ((1/(2∙4))+(1/(5∙7))+...+(1/((3n−1)(3n+1)))) |
| lim_(x→∞) (((x)^(1/4) −(x)^(1/6) )/( (x)^(1/4) +(x)^(1/6) ))=? |
| lim_(x→∞) ((x^6 −x^5 ))^(1/6) −((x^6 +5x^5 ))^(1/6) =? |
| a_n =a_(n−1) +((x−a_(n−1) )/t) lim_(n→∞) a_n =? |
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| 0<c<1 such that the recursive sequence {a_n } defined by setting a_(1 ) = (c/2) , a_(n+1) = (1/2)(c+a_n ^2 ) for n∈ N monotonic and convergent |
| lim_(n→∞) [Σ_(r=1) ^n (1/2^r )] where [•] greatest integer finction |
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| show that the sequence {a_n } defined recurssively by a_1 = (3/2) a_(n ) = (√(3a_(n−1 ) −2 )) for n≥2 converges and find its limit. |
| lim_(x→0) ((sin x−tan x)/x^3 ) |
| prove lim_(n→∞) ∫_0 ^1 (n/(1+n^2 x^2 ))e^x^2 dx=(π/2). |
| lim_(x→∞) ((√(x+(√(x+(√x)))))/( (√(x+1))))=? |
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| L=lim_(x→0) {(1/x^2 )tan^(−1) ((√(1+(x^2 /a^2 )))−1)} |
| Notation : Soit A une partie de R. On appelle indicatrice de A, note^ e χ_A , l′application x { ((1 si x ∈ A)),((0 sinon)) :}. 1. Pour k dans N^∗ notons f_k : x (cos x)^(2k) . Montrer que (f_k )_(k∈N^∗ ) converge vers χ_(πZ) . 2. Soit n un parame^ tre fixe^ dans N. Pour k dans N^∗ notons g_k : x f_k (n!πx). Montrer que (g_k )_(k∈N^∗ ) converge vers une application g^((n)) a^ de^ terminer, de^ pendante du parame^ tre n. E^ crire g^((n)) sous la forme χ_A ou^ A est une partie de R a^ de^ terminer. 3. Montrer que la suite de fonctions (g^((n)) )_(n∈N) converge vers χ_Q . 4. Soit x dans R. Calculer lim_(n→∞) (lim_(k→∞) (cos(n!πx))^(2k) ). |
| lim_(x→∞) [(x^(.1) −x^(.9) )^(1o) −x] |
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