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Question Number 197851 Answers: 0 Comments: 0

If z_1 = (√((α−β)/2)) and z_2 = (√((α+β)/2)) . Show that ∣z_1 −z_2 ∣^2 + ∣z_1 +z_2 ∣ = 2∣z∣^2 +∣z_2 ∣^2 and deduce that ∣α+(√(α^2 −β^2 ))∣ + ∣α−(√(α^2 −β^2 ))∣ = ∣α+β∣ + ∣α−β∣ Thank you in advance

$If z_{1} = \sqrt{\frac{α - β}{2}} and z_{2} = \sqrt{\frac{α + β}{2}} . Show$ $that ∣ z_{1} - z_{2} ∣^{2} + ∣ z_{1} + z_{2} ∣ = 2 ∣ z ∣^{2} + ∣ z_{2} ∣^{2} and$ $deduce that$ $∣ α + \sqrt{α^{2} - β^{2}} ∣ + ∣ α - \sqrt{α^{2} - β^{2}} ∣ = ∣ α + β ∣ + ∣ α - β ∣$ $Thank you in advance$

Question Number 197850 Answers: 1 Comments: 0

Solve the equation: (2sin x − 1)(2cos 2x + 2sin x +1) = 3(1−2cos 2x)

$S o l v e t h e e q u a t i o n :$ $(2 s i n x - 1) (2 c o s 2 x + 2 s i n x + 1) = 3 (1 - 2 c o s 2 x)$

Question Number 197848 Answers: 4 Comments: 0

Question Number 197847 Answers: 2 Comments: 0

If (x−1)^2 +(y−(√3))^2 <1, then find the range of ((x+y)/( (√(x^2 +y^2 )))).

$If {(x - 1)}^{2} + {(y - \sqrt{3})}^{2} < 1, then find the range of$ $\frac{x + y}{\sqrt{x^{2} + y^{2}}} .$

Question Number 197843 Answers: 0 Comments: 2

Exercice 2

$Exercice 2$

Question Number 197838 Answers: 2 Comments: 0

Question Number 197832 Answers: 1 Comments: 0

lim_(x→∞) ((2+(√(cosx)))/(−1+(√(cosx))))=?

$\lim_{x \to \infty} \frac{2 + \sqrt{c o s x}}{- 1 + \sqrt{c o s x}} = ?$

Question Number 197834 Answers: 2 Comments: 0

Question Number 197822 Answers: 1 Comments: 2

find maximum of ∣z^2 +2z−3∣ ?

$f i n d m a x i m u m o f ∣ z^{2} + 2 z - 3 ∣ ?$

Question Number 197821 Answers: 1 Comments: 0

find the value of : Ω = ∫_0 ^( 1) (( ln ( 1+ (1/x^( 2) ) ))/(2 + x^( 2) )) dx = ?

$f i n d t h e v a l u e o f :$ $Ω = \int_{0}^{1} \frac{\ln (1 + \frac{1}{x^{2}})}{2 + x^{2}} d x = ?$

Question Number 197819 Answers: 1 Comments: 0

find the value of : 𝛗 = Σ_(n=1) ^∞ (( (−1)^(n−1) H_( 2n) )/n) = ? where,H_n =1+(1/2) +(1/3) +...+(1/n)

$f i n d t h e v a l u e o f :$ $ϕ = \underset{n = 1}{\sum^{\infty}} \frac{{(- 1)}^{n - 1} H_{2 n}}{n} = ?$ $w h e r e, H_{n} = 1 + \frac{1}{2} + \frac{1}{3} + . . . + \frac{1}{n}$

Question Number 197808 Answers: 1 Comments: 1

prove lim_(n→∞) x^n = 0 when ∣x∣ < 1

$p r o v e \underset{n \to \infty}{l i m} x^{n} = 0 w h e n ∣ x ∣ < 1$

Question Number 197802 Answers: 1 Comments: 0

I=∫_(−2) ^6 ((∣x−1∣)/(x−1)) dx =?

$I = \underset{- 2}{\int^{6}} \frac{∣ x - 1 ∣}{x - 1} dx = ?$

Question Number 197906 Answers: 1 Comments: 0

S= Σ_(k=1) ^∞ (( Γ^( 2) ( k ))/(k Γ (2k ))) = ? −−−−

$S = \underset{k = 1}{\sum^{\infty}} \frac{Γ^{2} (k)}{k Γ (2 k)} = ?$ $- - - -$

Question Number 197795 Answers: 2 Comments: 0

Question Number 197794 Answers: 1 Comments: 0

if x = log tan((π/4)+(y/2)), prove that y = −ilog tan(((ix)/2) + (π/4)) here i = (√(−1))

$if x = \log \tan (\frac{π}{4} + \frac{y}{2}), prove that$ $y = - i \log \tan (\frac{i x}{2} + \frac{π}{4}) here i = \sqrt{- 1}$

Question Number 197792 Answers: 2 Comments: 0

Solve the following differential equation 1) y′′ + y = e^x + x^3 , y(0)=2, y′(0)=0 2) y′′ + y^′ − 2y = x + sin2x, y(0)=1, y′(0)=0 3) y′′ − y′ = xe^x , y(0)=2, y′(0)= 1 Thank you

$Solve the following differential equation$ $1) y^{″} + y = e^{x} + x^{3}, y (0) = 2, y^{'} (0) = 0$ $2) y^{″} + y^{^{'}} - 2 y = x + \sin 2 x, y (0) = 1, y^{'} (0) = 0$ $3) y^{″} - y^{'} = {xe}^{x}, y (0) = 2, y^{'} (0) = 1$ $Thank you$