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Question Number 169736 Answers: 0 Comments: 0

Given a ∈ [((3π)/2);2π]. Determinate a values for which the sequence u_n =cos(a)(sin(a))^n is constant from a certain value of n.

$${Given}\:{a}\:\in\:\left[\frac{\mathrm{3}\pi}{\mathrm{2}};\mathrm{2}\pi\right]. \\ $$$${Determinate}\:{a}\:{values}\:{for}\:{which} \\ $$$${the}\:{sequence}\:{u}_{{n}} ={cos}\left({a}\right)\left({sin}\left({a}\right)\right)^{{n}} \:{is} \\ $$$${constant}\:{from}\:{a}\:{certain}\:{value}\:{of}\:{n}. \\ $$

Question Number 169733 Answers: 1 Comments: 0

Question Number 169727 Answers: 0 Comments: 6

Question Number 169725 Answers: 0 Comments: 0

Question Number 169760 Answers: 1 Comments: 0

Find x (5 - 2x)(5 + 2 (√(4 - 2x^2 ))) = 25

$$\mathrm{Find}\:\:\boldsymbol{\mathrm{x}} \\ $$$$\left(\mathrm{5}\:-\:\mathrm{2x}\right)\left(\mathrm{5}\:+\:\mathrm{2}\:\sqrt{\mathrm{4}\:-\:\mathrm{2x}^{\mathrm{2}} }\right)\:=\:\mathrm{25} \\ $$

Question Number 169751 Answers: 0 Comments: 0

find the forier transform of g(t)=cos^2 (2π f_c t)

$${find}\:\:{the}\:{forier}\:{transform}\:{of} \\ $$$${g}\left({t}\right)=\mathrm{cos}^{\mathrm{2}} \left(\mathrm{2}\pi\:\mathrm{f}_{\mathrm{c}} \:\mathrm{t}\right)\:\:\: \\ $$

Question Number 169745 Answers: 2 Comments: 0

Question Number 169743 Answers: 2 Comments: 0

lim_(x→0) ((∫_0 ^( x) (√(1 + sin t)) dt)/x) = a , then a^2 − 1 = ... ?

$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\:\frac{\underset{\mathrm{0}} {\int}\overset{\:{x}} {\:}\sqrt{\mathrm{1}\:+\:\mathrm{sin}\:{t}}\:{dt}}{{x}}\:=\:{a}\:\:,\:\: \\ $$$${then}\:\:\:{a}^{\mathrm{2}} \:−\:\mathrm{1}\:\:=\:\:...\:? \\ $$

Question Number 169713 Answers: 0 Comments: 4

Question Number 169712 Answers: 0 Comments: 0

Question Number 169711 Answers: 2 Comments: 3

prove that: lim_( x → 0) ( (1/x^( 2) ) − (e^( x) /((e^( x) −1 )^( 2) )) ) = (1/(12))

$$ \\ $$$$\:\:\:\:{prove}\:{that}: \\ $$$$\:\: \\ $$$$\:\:{lim}_{\:{x}\:\rightarrow\:\mathrm{0}} \left(\:\frac{\mathrm{1}}{{x}^{\:\mathrm{2}} }\:\:−\:\frac{{e}^{\:{x}} }{\left({e}^{\:{x}} −\mathrm{1}\:\right)^{\:\mathrm{2}} }\:\right)\:=\:\frac{\mathrm{1}}{\mathrm{12}} \\ $$$$\:\:\:\:\:\: \\ $$

Question Number 169808 Answers: 0 Comments: 0

If the Real component of an analytic function is given by log_e (x^2 +y^2 )^(1/2) , find the function. Mastermind

$${If}\:{the}\:{Real}\:{component}\:{of}\:{an}\:{analytic} \\ $$$${function}\:{is}\:{given}\:{by}\:{log}_{{e}} \left({x}^{\mathrm{2}} +{y}^{\mathrm{2}} \right)^{\frac{\mathrm{1}}{\mathrm{2}}} , \\ $$$${find}\:{the}\:{function}. \\ $$$$ \\ $$$${Mastermind} \\ $$

Question Number 169706 Answers: 0 Comments: 0

using cylindrical coordinates { ((x=rcosθ)),((y = rsin θ)),((z=z)) :} to evaluate the integral K= ∫∫∫_S (√(x^2 +y^2 −z^2 )) dxdydz where S= {(x,y,z) ∈R^3 : x^2 +y^2 ≤ 4, 0 ≤z≤(√(x^2 +y^2 ))}

$$\mathrm{using}\:\mathrm{cylindrical}\:\mathrm{coordinates}\:\begin{cases}{{x}={r}\mathrm{cos}\theta}\\{{y}\:=\:{r}\mathrm{sin}\:\theta}\\{{z}={z}}\end{cases} \\ $$$$\mathrm{to}\:\mathrm{evaluate}\:\mathrm{the}\:\mathrm{integral} \\ $$$${K}=\:\int\int\int_{{S}} \sqrt{{x}^{\mathrm{2}} +{y}^{\mathrm{2}} −{z}^{\mathrm{2}} }\:{dxdydz} \\ $$$$\mathrm{where} \\ $$$$\:{S}=\:\left\{\left({x},{y},{z}\right)\:\in\mathbb{R}^{\mathrm{3}} :\:{x}^{\mathrm{2}} +{y}^{\mathrm{2}} \:\leqslant\:\mathrm{4},\:\mathrm{0}\:\leqslant{z}\leqslant\sqrt{{x}^{\mathrm{2}} +{y}^{\mathrm{2}} }\right\} \\ $$

Question Number 169807 Answers: 0 Comments: 0

Given that U=x^4 −6x^2 y^2 +y^4 , find v and w such that w=u+iv is analytic Mastermind

$${Given}\:{that}\:{U}={x}^{\mathrm{4}} −\mathrm{6}{x}^{\mathrm{2}} {y}^{\mathrm{2}} +{y}^{\mathrm{4}} ,\:{find} \\ $$$${v}\:{and}\:{w}\:{such}\:{that}\:{w}={u}+{iv}\:{is}\:{analytic} \\ $$$$ \\ $$$${Mastermind} \\ $$

Question Number 169702 Answers: 1 Comments: 0

determinant ((0,4,1,1),(4,0,0,1),(3,5,2,1),(2,2,5,1))=

$$\begin{vmatrix}{\mathrm{0}}&{\mathrm{4}}&{\mathrm{1}}&{\mathrm{1}}\\{\mathrm{4}}&{\mathrm{0}}&{\mathrm{0}}&{\mathrm{1}}\\{\mathrm{3}}&{\mathrm{5}}&{\mathrm{2}}&{\mathrm{1}}\\{\mathrm{2}}&{\mathrm{2}}&{\mathrm{5}}&{\mathrm{1}}\end{vmatrix}=\: \\ $$

Question Number 169774 Answers: 1 Comments: 3

Question Number 169771 Answers: 3 Comments: 0

(1/(1+cos^2 x)) + (1/(sin^2 x+1)) = ((48)/(35))

$$\:\:\:\:\:\:\frac{\mathrm{1}}{\mathrm{1}+\mathrm{cos}\:^{\mathrm{2}} {x}}\:+\:\frac{\mathrm{1}}{\mathrm{sin}\:^{\mathrm{2}} {x}+\mathrm{1}}\:=\:\frac{\mathrm{48}}{\mathrm{35}} \\ $$

Question Number 169770 Answers: 0 Comments: 4

Question Number 169677 Answers: 2 Comments: 0

M = ∫ (dx/((x−4)(√(x^2 −6x+8)))) =?

$$\:\:\:\:{M}\:=\:\int\:\frac{{dx}}{\left({x}−\mathrm{4}\right)\sqrt{{x}^{\mathrm{2}} −\mathrm{6}{x}+\mathrm{8}}}\:=? \\ $$

Question Number 169671 Answers: 0 Comments: 0

Question Number 169669 Answers: 1 Comments: 0

Question Number 169668 Answers: 0 Comments: 1

Question Number 169667 Answers: 1 Comments: 0

find the domain of (i) (x/( (√(x+5)))) (ii) (√x)+2 (iii) (3/( (√(x+2))+5))

$$\boldsymbol{{find}}\:\boldsymbol{{the}}\:\boldsymbol{{domain}}\:\boldsymbol{{of}} \\ $$$$\left(\boldsymbol{{i}}\right)\:\frac{\boldsymbol{{x}}}{\:\sqrt{\boldsymbol{{x}}+\mathrm{5}}} \\ $$$$\left(\boldsymbol{{ii}}\right)\:\sqrt{\boldsymbol{{x}}}+\mathrm{2} \\ $$$$\left(\boldsymbol{{iii}}\right)\:\frac{\mathrm{3}}{\:\sqrt{\boldsymbol{{x}}+\mathrm{2}}+\mathrm{5}} \\ $$

Question Number 169664 Answers: 1 Comments: 0

Given that n(A)=10 and n(B)=6 i) what is the largest possible of n(A∪B) ii) what is the smallest possible value of n(A∪B) iii) what is the smallest possible value of n(A∩B)

Question Number 169658 Answers: 1 Comments: 2

Question Number 169655 Answers: 1 Comments: 0

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