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calculate ∫_0 ^∞ (dx/(x^(2 ) +(√(1+x^2 )))) . |
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If x ∈R show that (2+i)e^((1+3i)) +(2−i)e^((1−3i)) is also real. |
Which of the following expressions are positive for all real values of x? a) x^2 − 2x + 5 b) x^2 −2x−1 c) x^2 +4x+2 d) 2x^2 −6x + 5 |
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Two plane mirrors are inclined at an angle of 30°.A ray of light which makes an angle of incidence of 50° with one of the mirrors,undergoes two successive reflections at the mirrors.Calculate the angle of deviation. please help....its urgent |
n∈N U_(n+1) =((1/2))^(n+1) +U_n U_n =? |
f : N → R g : N → R f(n)=∫_0 ^(2π) x^n sin x dx g(n)=∫_0 ^(2π) x^n cos x dx ((f(n+1)−f(n))/(g(n+1)−g(n)))=? |
If y=4x^2 −1 , then find ((85)/(169))+Σ_(i=1) ^(84) (1/(y(i))) |
In △ABC, if sin A=sin^2 B then prove 4 cos 2A−4 cos 2B=1−cos 4B |
Solve the diferential equatuion (dy/dx)=((2x+y+1)/(x−2y+3)) |
Evaluate : the Integral ∫_(-(π/2)) ^(π/2) ∫_0 ^(3 cos θ) r^2 sin^2 θ. dr dθ |
the function f(x) is defined by f(x) = { ((−x + 1 , for x≤3)),((kx − 8 , for x ≥ 3)) :} find the value of k . |
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ind the value of f(a) =∫_0 ^(+∞) (dx/(x^2 +(√(a^2 +x^2 )))) dx witha>0 2)calculate f^′ (a) . |
let f(x)= (1+e^(−x) )^n 1) calculate f^((p)) (x) and f^((p)) (o) 2)calculate f^((n)) (0) 3)developp f at integr serie . |
calculate f(λ) = ∫_0 ^(+∞) e^(−λx) cos(π[x])dx withλ>0 |
let I_n = ∫_0 ^n (((−1)^([x]) )/((2x+1)^2 ))dx 1) calculate I_n interms of n 2) find lim_(n→+∞) I_n |
calculate A_n =∫_0 ^n (x−[(√x)])dx and lim_(n→+∞) A_n |
find nature of the serie Σ_(n=1) ^∞ (Σ_(k=0) ^n (1/C_n ^k ))x^n |
calculate ∫_0 ^1 (√(x+(√(x+1)))) dx . |
let f(x)=(√(x+(√(x+1)))) 1) find D_f 2) give the equation of assymtote at point A(0,f(o)) 3) if f(x)∼ a(x−1) +b (x→1) determine a andb 4) calculate f^′ (x) 5) find f^(−1) (x) and (f^(−1) )^′ (x) |
calculate B_n = Σ_(k=0) ^n (−1)^k (2k^2 +1) interms of n. |
calculate A_n = Σ_(k=0) ^n (−1)^k (2k+3) interms of n |
calculate ∫_0 ^∞ ((arctan(2x))/x) e^(−tx) dx with t ≥0 |
Pg 1632 Pg 1633 Pg 1634 Pg 1635 Pg 1636 Pg 1637 Pg 1638 Pg 1639 Pg 1640 Pg 1641 |