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Question Number 81158 Answers: 0 Comments: 0

S=(1/(cos1))+(1/(cos1cos2))+......+(1/(cos87cos88)) K=tan1tan2+tan3tan4+......+tan87tan88

$${S}=\frac{\mathrm{1}}{{cos}\mathrm{1}}+\frac{\mathrm{1}}{{cos}\mathrm{1}{cos}\mathrm{2}}+......+\frac{\mathrm{1}}{{cos}\mathrm{87}{cos}\mathrm{88}} \\ $$$${K}={tan}\mathrm{1}{tan}\mathrm{2}+{tan}\mathrm{3}{tan}\mathrm{4}+......+{tan}\mathrm{87}{tan}\mathrm{88} \\ $$

Question Number 81157 Answers: 0 Comments: 0

Let n≥2 , for x∈[0,1] : let consider A(x)={ u∈R_+ ^∗ \ x<u^n } 1)Prove that if a,b∈[0,1] a≤b ⇔A(a)⊆A(b) 2)Deduce x=[infA(x) ]^n

$${Let}\:{n}\geqslant\mathrm{2}\:,\:{for}\:\:{x}\in\left[\mathrm{0},\mathrm{1}\right]\:\::\:\:\:{let}\:\:{consider}\:\:{A}\left({x}\right)=\left\{\:{u}\in\mathbb{R}_{+} ^{\ast} \:\backslash\:\:\:{x}<{u}^{{n}} \right\}\: \\ $$$$\left.\mathrm{1}\right){Prove}\:\:{that}\:{if}\:\:\:{a},{b}\in\left[\mathrm{0},\mathrm{1}\right]\:\:\:\:\:\:\:\:\:\:{a}\leqslant{b}\:\Leftrightarrow{A}\left({a}\right)\subseteq{A}\left({b}\right)\:\:\: \\ $$$$\left.\mathrm{2}\right){Deduce}\:\:\:\:\:{x}=\left[{infA}\left({x}\right)\:\right]^{{n}} \:\: \\ $$

Question Number 81149 Answers: 1 Comments: 0

Question Number 81139 Answers: 1 Comments: 6

Question Number 81133 Answers: 0 Comments: 1

find this ∫(1/(sin^2 x((cot^4 x))^(1/7) ))dx

$${find}\:{this}\: \\ $$$$\int\frac{\mathrm{1}}{{sin}^{\mathrm{2}} {x}\sqrt[{\mathrm{7}}]{{cot}^{\mathrm{4}} {x}}}{dx} \\ $$

Question Number 81134 Answers: 0 Comments: 0

prove A×B≠B×A with A and B are matrices

$${prove}\:{A}×{B}\neq{B}×{A} \\ $$$${with}\:{A}\:{and}\:{B}\:{are}\:{matrices} \\ $$

Question Number 81135 Answers: 1 Comments: 1

Question Number 81130 Answers: 0 Comments: 0

ζ(s)=0

$$\zeta\left({s}\right)=\mathrm{0} \\ $$

Question Number 81124 Answers: 1 Comments: 0

Question Number 81123 Answers: 0 Comments: 3

Question Number 81122 Answers: 1 Comments: 4

Question Number 81104 Answers: 0 Comments: 4

(a^ ×b^ ).c^ = (a×c) . (b×c). it right?

$$\left(\bar {{a}}\:×\bar {{b}}\:\right).\bar {{c}}\:=\:\left({a}×{c}\right)\:.\:\left({b}×{c}\right).\:{it}\:{right}? \\ $$

Question Number 81115 Answers: 0 Comments: 0

e^x ∫((2csec^2 θ dθ)/([4+(2tanθ)^2 ]^(3/2) )) = e^x ∫((2csec^2 θ dθ)/([4+(2tanθ)^2 ]^(3/2) )) =

$$\mathrm{e}^{\mathrm{x}} \int\frac{\mathrm{2}{csec}^{\mathrm{2}} \theta\:{d}\theta}{\left[\mathrm{4}+\left(\mathrm{2}{tan}\theta\right)^{\mathrm{2}} \right]^{\mathrm{3}/\mathrm{2}} }\:\:= \\ $$$$\mathrm{e}^{\mathrm{x}} \int\frac{\mathrm{2}{csec}^{\mathrm{2}} \theta\:{d}\theta}{\left[\mathrm{4}+\left(\mathrm{2}{tan}\theta\right)^{\mathrm{2}} \right]^{\mathrm{3}/\mathrm{2}} }\:\:= \\ $$

Question Number 81100 Answers: 0 Comments: 2

∫ ((x dx)/((tan x+cot x)^2 )) = ?

$$\int\:\frac{{x}\:{dx}}{\left(\mathrm{tan}\:{x}+\mathrm{cot}\:{x}\right)^{\mathrm{2}} }\:=\:? \\ $$

Question Number 81096 Answers: 1 Comments: 1

lim_(x→3) (((sin x)/(sin 3)))^(1/(x−3)) =?

$$\underset{{x}\rightarrow\mathrm{3}} {\mathrm{lim}}\:\left(\frac{\mathrm{sin}\:{x}}{\mathrm{sin}\:\mathrm{3}}\right)^{\frac{\mathrm{1}}{{x}−\mathrm{3}}} \:=? \\ $$

Question Number 81092 Answers: 0 Comments: 2

Question Number 81091 Answers: 0 Comments: 2

Question Number 81075 Answers: 2 Comments: 1

Question Number 81062 Answers: 0 Comments: 5

cos x (√(1+sin x−2cos x)) = cos x−sin x in [ −5π , −((7π)/2)]

$$\mathrm{cos}\:{x}\:\sqrt{\mathrm{1}+\mathrm{sin}\:{x}−\mathrm{2cos}\:{x}}\:=\:\mathrm{cos}\:{x}−\mathrm{sin}\:{x} \\ $$$${in}\:\left[\:−\mathrm{5}\pi\:,\:−\frac{\mathrm{7}\pi}{\mathrm{2}}\right]\: \\ $$

Question Number 81057 Answers: 0 Comments: 7

solve in [−π;π] (E): sin3x=−sin2x

$${solve}\:\mathrm{in}\:\left[−\pi;\pi\right]\: \\ $$$$\left({E}\right):\:{sin}\mathrm{3}{x}=−{sin}\mathrm{2}{x} \\ $$

Question Number 81054 Answers: 0 Comments: 2

solve the differential equation (a)(d^2 y/dx^2 )=sin^2 (x+y) (b)(d^2 y/dx^2 )=cos (x+y)

$${solve}\:{the}\:{differential} \\ $$$${equation} \\ $$$$\left({a}\right)\frac{{d}^{\mathrm{2}} {y}}{{dx}^{\mathrm{2}} }=\mathrm{sin}\:^{\mathrm{2}} \left({x}+{y}\right) \\ $$$$\left({b}\right)\frac{{d}^{\mathrm{2}} {y}}{{dx}^{\mathrm{2}} }=\mathrm{cos}\:\left({x}+{y}\right) \\ $$

Question Number 81043 Answers: 1 Comments: 8

∫ ((2e^(2x) −e^x )/(√(3e^(2x) −6e^x −1))) dx

$$\int\:\frac{\mathrm{2}{e}^{\mathrm{2}{x}} −{e}^{{x}} }{\sqrt{\mathrm{3}{e}^{\mathrm{2}{x}} −\mathrm{6}{e}^{{x}} −\mathrm{1}}}\:{dx} \\ $$

Question Number 81039 Answers: 0 Comments: 2

((log_( 0,2) (x−2))/((4^x −8)(∣x∣−5))) ≥ 0

$$\frac{\mathrm{log}_{\:\mathrm{0},\mathrm{2}} \left({x}−\mathrm{2}\right)}{\left(\mathrm{4}^{{x}} −\mathrm{8}\right)\left(\mid{x}\mid−\mathrm{5}\right)}\:\geqslant\:\mathrm{0} \\ $$

Question Number 81027 Answers: 0 Comments: 6

calculate lim_(x→0) ((tan(2x)−2tanx−2tan^3 x)/x^5 )

$${calculate}\:{lim}_{{x}\rightarrow\mathrm{0}} \:\frac{{tan}\left(\mathrm{2}{x}\right)−\mathrm{2}{tanx}−\mathrm{2}{tan}^{\mathrm{3}} {x}}{{x}^{\mathrm{5}} } \\ $$

Question Number 81011 Answers: 0 Comments: 6

Question Number 81010 Answers: 0 Comments: 4

show that (cosθ−i sinθ)^n =(cosnθ−i sinθ)

$${show}\:{that} \\ $$$$\left({cos}\theta−{i}\:{sin}\theta\right)^{{n}} =\left({cosn}\theta−{i}\:{sin}\theta\right) \\ $$

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