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find lim_(x→0) ((sin(sh(2x))−sh(sin(3x)))/x^2 ) |
find ∫_0 ^1 (dx/(((√x)+(√(x+1)))^3 )) |
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calculate Σ_(n=0) ^∞ arctan(((2n+1)/(n^4 +2n^3 +n^2 +1))) |
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we have z = e^(((2pi)/7)i) a = z+ z^2 + z^4 and b = z^3 + z^5 +z^6 we know a + b = −1 and 1−b=a find S = cos(((2pi)/7))+ cos(((4pi)/7)) + cos(((8pi)/7)) thanks for help |
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if q≥1 and x>−1 then: (1+x)^q ≥ (1+x)^(q−1) + x ≥ 1+qx |
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consider the circle (x−1)^2 +(y−1)^2 =2, A(1,4), B(1,−5). if P is a point on the circle such that PA+PB is maximum then prove that P,A,B are collinear points. |
Soit X une variable aleatoire de loi geometrique de parametre p∈]0.1[ calculer P({X≥4}) |
On dispose de N+1 urnes.l′urne U_k contient k boules blanches et N−k boules noires.on tire successivement sans remise n boules de l′urne et on note An l′evenement ′′choisir n boules noires lors des n premiers tirages′′. Determiner P(An). on notera U_k =′′choisir l′urne k′′ |
Let a≥b≥c≥0 and a^2 +b^2 +c^2 = 3. Prove that a^3 +(b+c)^3 ≤ 9 |
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(5^(log _(5/3) (5)) /3^(log _(5/3) (3)) ) =? |
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Solve the equation: cos(6x)−cos(4x)=4y^2 +4y+3 |
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If ((!6)/x) −!4 = !x then x =? |
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if f(ax+2b)=x and f(2a)=(b/a) find f(5b)=? |
Σ_(n=2) ^∞ ((1/(2n^2 −2)))=? |
∫_0 ^∞ (x−(x^3 /2)+(x^5 /(2∙4))−(x^7 /(2∙4∙6))+...)∙(1+(x^2 /2^2 )+(x^4 /(2^2 ∙4^2 ))+(x^6 /(2^2 ∙4^2 ∙6^2 ))+...)dx=(√e) |
Pg 675 Pg 676 Pg 677 Pg 678 Pg 679 Pg 680 Pg 681 Pg 682 Pg 683 Pg 684 |