# Question and Answers Forum

AllQuestion and Answers: Page 10

z′ = (1/2)(z+(1/z)) z and z′ are complex numbers show that z = 2e^(iθ) show that M′ describes a conic section
If a^x = b^y (a/x) + (b/y) = 1 then, a^x + b^y = ?
∫_0 ^( ∞) ((ln^2 x)/(1+x^4 )) dx
a, b>0. 2a+b=1, prove that ((a^2 +b^2 )/(2a))+((2a)/b^2 ) > 2.
Evaluate and leave your answer in exponent form. 5^(2024) − 5^(2023) − 5^(2022) − 5^(2021) − 5^(2020) − 5^(2019) = ?
An aeroplane flies 25 km in the direction 60° North of East 35 km Straight East, then 15 km straight North. What direction is the pane from the straight point?
What is the smallest number which must added to 9454351626 so that it will become divisible by 11?
Calculate the area enclosed by the curve ((1/x)−2)^2 +((1/y)−2)^2 =1
Find: ((61^3 + 24^3 )/(61^3 + 37^3 )) = ?
Compare it: a = log_3 4 b = log_5 6 c = log_6 2
If f(x) = (((2a + 1)∙x + 1)/(x − a)) and f(x) = f^(−1) (x) Find: a^2 + 3 = ?
u_(n+1) = u_n −u_n ^3 , u_0 ∈]0,1[ v_n = (1/u_(n+1) ^2 )−(1/u_n ^2 ) = f(u_n ^2 ) ; f(x) = ((2−x)/((1−x)^2 )) v_n converges to 2, v_n is decreasing . show that v_n ≥ 2 x_n =(1/(n+1))Σ_(m=0) ^m (v_m ) . show that x_0 ≥x_n ≥v_n . show that x_n is decreasing and lim_(n→∞) x_n = l ≥2 . show that 2x_(n+1) −x_n ≤v_(n+1) and deduce l . express x_(n+1) −x_n interms of u_n . deduce lim_(n→∞) nu_n ^2

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