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OthersQuestion and Answers: Page 44
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OthersQuestion and Answers: Page 44 |
| (1/(998))+(1/(998.1995))+(1/(998.1995.2992))+(1/(998.1995.2992.3989))+...=(1/(997)) |
| Σ_(n=1) ^n nsin(n) |
| If P = 2 + (1/P) then what is the answer of P^2 − (1/P^2 ) ? |
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| What will be the minimum area of a heptagon inscribed in an unit square? |
| (2+(π/e))(((17)/(16))+(π/(4e)))(((82)/(81))+(π/(9e)))(((257)/(256))+(π/(16e)))... |
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| Σ_(n=1) ^∞ ((cos((π+e)n))/n^4 ) |
| ((sin1)/e)−((sin(2))/(2e^2 ))+((sin(3))/(3e^3 ))−((sin(4))/(4e^4 ))+...=tan^(−1) (((sin(1))/(cos(1)+e))) |
| A particle performs simple harmonic motion between two points A and B which are 10 m apart on a horizontal straight line. When the particle is 3 m away from the centre, O, of the line AB, its speed is 8 ms^(−1) . Find the least time required for the particle to move from B to the midpoint of OA. |
| we consider that application n≥1 det : M_n (R)→R A det(A) 1−verify that ∀H∈M_n (R) and t∈R if A=I_n ⇒det(A+tH)=1+t.Tr(H)+○(t) 2−suppose that: A∈GL_n (R) prouve that the differntial of det in A is given by: H Tr[(com(A))^T H] Tr: trace of matrix (com(A))^T : transpose of the comatrix |
| ((sin(√π))/1^3 )+((sin(√(4π)))/2^3 )+((sin(√(9π)))/3^3 )+((sin(√(16π)))/4^3 )+....=((π(√π))/(12))(1−3(√π)+2π) |
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| 1+(1/1^2 )((1/(2.1!)))+(1/3^2 )(((1.3)/(2^2 .2!)))+(1/5^2 )(((1.3.5)/(2^3 .3!)))+...=(π/2)log(2) |
| Σ_(n=1) ^∞ ((cos((n/π)))/n^4 )=−(1/(48π^4 ))+(1/(12))(1−(1/π^2 ))+(π^4 /(90)) |
| Find x : sin(3x)−sin(2x)−2sin(x) = (√3)cos(x) |
| Σ_(n=1) ^∞ ((sinn)/n^3 ) |
| Find modulus and argumen of z = (((1−i)^4 ((√3)+i)^7 )/((1+i(√2))^8 (−1−i(√3))^(12) )) |
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| ∫_0 ^∞ ((cos(xπt))/(cosh(πx)))e^(−π^2 x) dx |
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| (1/1^3 )−(1/2^3 )+(1/4^3 )−(1/5^3 )+(1/7^3 )−(1/8^3 )+... |
| If f(x)=8x^(3 ) +3x then lim_(x→∞) (x^(1/3) /(f^(−1) (8x)−f^(−1) (x))) is |
| Σ_(n=1) ^∞ ((cos(n))/n^2 ) |