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Question Number 205107 Answers: 0 Comments: 2

y = log_2 (sin(x)+cos(x)) ⇒ R_y = ?(Range )

$$ \\ $$$$\:\:\:\:{y}\:=\:{log}_{\mathrm{2}} \left({sin}\left({x}\right)+{cos}\left({x}\right)\right) \\ $$$$\:\:\:\Rightarrow\:\:{R}_{{y}} \:=\:?\left({Range}\:\right) \\ $$$$ \\ $$

Question Number 205106 Answers: 1 Comments: 1

Question Number 205101 Answers: 1 Comments: 0

given that there are real constant a,b, c, d such the identity λx^2 +2xy+y^2 = (ax+by)^2 +(cx+dy)^2 holds for all x,y ∈ R this implies (a) λ=−5 (b) λ≥1 (c)0<λ<1 (d) there is no such λ∈R

$$\:\:\mathrm{given}\:\mathrm{that}\:\mathrm{there}\:\mathrm{are}\:\mathrm{real}\:\mathrm{constant}\:\mathrm{a},\mathrm{b},\:\mathrm{c},\:\mathrm{d} \\ $$$$\:\:\mathrm{such}\:\mathrm{the}\:\mathrm{identity} \\ $$$$\:\lambda\mathrm{x}^{\mathrm{2}} +\mathrm{2xy}+\mathrm{y}^{\mathrm{2}} =\:\left(\mathrm{ax}+\mathrm{by}\right)^{\mathrm{2}} +\left(\mathrm{cx}+\mathrm{dy}\right)^{\mathrm{2}} \:\mathrm{holds} \\ $$$$\:\mathrm{for}\:\mathrm{all}\:\mathrm{x},\mathrm{y}\:\in\:\mathbb{R}\:\mathrm{this}\:\mathrm{implies} \\ $$$$\left({a}\right)\:\lambda=−\mathrm{5}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left({b}\right)\:\lambda\geqslant\mathrm{1}\:\:\:\:\:\:\:\:\:\:\:\:\:\left({c}\right)\mathrm{0}<\lambda<\mathrm{1} \\ $$$$\:\left({d}\right)\:\mathrm{there}\:\mathrm{is}\:\mathrm{no}\:\mathrm{such}\:\lambda\in\mathbb{R} \\ $$

Question Number 205091 Answers: 0 Comments: 0

f:z ⇒ z f:z ⇒ z_n f:z_n ⇒ z_n How many homomorphism can be define

$${f}:{z}\:\Rightarrow\:{z} \\ $$$${f}:{z}\:\Rightarrow\:{z}_{{n}} \\ $$$${f}:{z}_{{n}} \Rightarrow\:{z}_{{n}} \\ $$$${How}\:{many}\:{homomorphism}\:{can}\:{be}\:{define} \\ $$

Question Number 205083 Answers: 1 Comments: 0

Question Number 205073 Answers: 6 Comments: 0

if a, b, c are the roots of f(x)=x^3 −2024x^2 +2024x+2024 find (1/(1−a^2 ))+(1/(1−b^2 ))+(1/(1−c^2 ))=?

$${if}\:{a},\:{b},\:{c}\:{are}\:{the}\:{roots}\:{of} \\ $$$${f}\left({x}\right)={x}^{\mathrm{3}} −\mathrm{2024}{x}^{\mathrm{2}} +\mathrm{2024}{x}+\mathrm{2024} \\ $$$${find}\:\frac{\mathrm{1}}{\mathrm{1}−{a}^{\mathrm{2}} }+\frac{\mathrm{1}}{\mathrm{1}−{b}^{\mathrm{2}} }+\frac{\mathrm{1}}{\mathrm{1}−{c}^{\mathrm{2}} }=? \\ $$

Question Number 205070 Answers: 0 Comments: 5

Given { ((A∩B= { a, b})),((A∩C = { b, c} )),((B∩C= { b ,d })) :} then (A∩C) + (A∩B) + (B∩C)

$$\:\:\:\mathrm{Given}\:\begin{cases}{\mathrm{A}\cap\mathrm{B}=\:\left\{\:\mathrm{a},\:\mathrm{b}\right\}}\\{\mathrm{A}\cap\mathrm{C}\:=\:\left\{\:\mathrm{b},\:\mathrm{c}\right\}\:}\\{\mathrm{B}\cap\mathrm{C}=\:\left\{\:\mathrm{b}\:,\mathrm{d}\:\right\}}\end{cases} \\ $$$$\:\:\:\:\mathrm{then}\:\left(\mathrm{A}\cap\mathrm{C}\right)\:+\:\left(\mathrm{A}\cap\mathrm{B}\right)\:+\:\left(\mathrm{B}\cap\mathrm{C}\right) \\ $$

Question Number 205092 Answers: 2 Comments: 0

Question Number 205062 Answers: 3 Comments: 0

Question Number 205055 Answers: 1 Comments: 0

(lim inf(A_n ))^c =limsup(A_n ^c ) prove

$$\left({lim}\:{inf}\left({A}_{{n}} \right)\right)^{{c}} \:={limsup}\left({A}_{{n}} ^{{c}} \right)\:\:\:\:\:{prove} \\ $$

Question Number 205051 Answers: 2 Comments: 0

Find all values of k such that the expression x^3 + kx^2 −7x+6 can be resolved into three linear real factors.

$$\mathrm{Find}\:\mathrm{all}\:\mathrm{values}\:\mathrm{of}\:\:\mathrm{k}\:\mathrm{such}\:\mathrm{that}\:\mathrm{the} \\ $$$$\mathrm{expr}{e}\mathrm{ssion}\:\mathrm{x}^{\mathrm{3}} +\:\mathrm{kx}^{\mathrm{2}} −\mathrm{7x}+\mathrm{6}\:\mathrm{can}\:\mathrm{be} \\ $$$$\mathrm{re}{s}\mathrm{olved}\:\mathrm{into}\:\mathrm{three}\:\mathrm{linear}\:\mathrm{real}\:\mathrm{factors}. \\ $$

Question Number 205054 Answers: 0 Comments: 1

prove (lim sup(A_n ))^c = lim inf(A_n ^c )

$${prove} \\ $$$$\left({lim}\:{sup}\left({A}_{{n}} \right)\right)^{{c}} =\:{lim}\:{inf}\left({A}_{{n}} ^{{c}} \right) \\ $$

Question Number 205053 Answers: 0 Comments: 1

Question Number 205045 Answers: 0 Comments: 4

$$\:\:\: \\ $$$$ \\ $$$$ \\ $$

Question Number 205032 Answers: 3 Comments: 1

Question Number 205024 Answers: 0 Comments: 0

Question Number 205021 Answers: 2 Comments: 0

x^2 + 5x +6 = 0 & x^2 + kx + 1 = 0 have a common root then k = ?

$${x}^{\mathrm{2}} \:+\:\mathrm{5}{x}\:+\mathrm{6}\:=\:\mathrm{0}\:\&\:{x}^{\mathrm{2}} \:+\:{kx}\:+\:\mathrm{1}\:=\:\mathrm{0}\:{have}\:{a}\: \\ $$$${common}\:{root}\:\mathrm{then}\:\:{k}\:=\:? \\ $$

Question Number 205018 Answers: 1 Comments: 2

For what value of ′k′ can be expression x^3 + kx^2 −7x +6 be resolved into three linear factors? (a) 0 (b) 1 (c) 2 (d) 3

$$\mathrm{For}\:\mathrm{what}\:\mathrm{value}\:\mathrm{of}\:\:'\mathrm{k}'\:\mathrm{can}\:\mathrm{be}\:\mathrm{expression}\:{x}^{\mathrm{3}} \:+\:{kx}^{\mathrm{2}} \:−\mathrm{7}{x}\:+\mathrm{6}\:\:\:\:\:\:\:\:\:\:\:\: \\ $$$$\mathrm{be}\:\mathrm{resolved}\:\mathrm{into}\:\mathrm{three}\:\mathrm{linear}\:\mathrm{factors}? \\ $$$$\left(\mathrm{a}\right)\:\mathrm{0}\:\:\:\:\:\:\:\:\:\:\:\left(\mathrm{b}\right)\:\mathrm{1}\:\:\:\:\:\:\:\:\:\:\:\:\:\left(\mathrm{c}\right)\:\mathrm{2}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left(\mathrm{d}\right)\:\mathrm{3} \\ $$

Question Number 205013 Answers: 2 Comments: 0

if y=(x)^(1/7) prove that y^′ =(1/(7 (x^6 )^(1/7) ))

$${if}\:{y}=\sqrt[{\mathrm{7}}]{{x}}\:{prove}\:{that} \\ $$$${y}^{'} =\frac{\mathrm{1}}{\mathrm{7}\:\sqrt[{\mathrm{7}}]{{x}^{\mathrm{6}} }} \\ $$

Question Number 205001 Answers: 2 Comments: 0

Question Number 204999 Answers: 2 Comments: 0

Solve for x∈C x^3 +(4−3i)x^2 −(51+49i)x−442+170i=0

$$\mathrm{Solve}\:\mathrm{for}\:{x}\in\mathbb{C} \\ $$$${x}^{\mathrm{3}} +\left(\mathrm{4}−\mathrm{3i}\right){x}^{\mathrm{2}} −\left(\mathrm{51}+\mathrm{49i}\right){x}−\mathrm{442}+\mathrm{170i}=\mathrm{0} \\ $$

Question Number 204994 Answers: 2 Comments: 0

Question Number 204991 Answers: 2 Comments: 1

Question Number 204992 Answers: 1 Comments: 0

Is there any way to integrate: ∫ (1/( (√(ln(x))))) dx without hitting the Gauss error function or e^t^2 and e^(−t^2 ) ?

$$\mathrm{Is}\:\mathrm{there}\:\mathrm{any}\:\mathrm{way}\:\mathrm{to}\:\mathrm{integrate}: \\ $$$$\int\:\frac{\mathrm{1}}{\:\sqrt{\mathrm{ln}\left({x}\right)}}\:{dx} \\ $$$$\mathrm{without}\:\mathrm{hitting}\:\mathrm{the}\:\mathrm{Gauss}\:\mathrm{error}\:\mathrm{function} \\ $$$$\mathrm{or}\:{e}^{{t}^{\mathrm{2}} } \:\mathrm{and}\:{e}^{−{t}^{\mathrm{2}} } \:? \\ $$

Question Number 204985 Answers: 1 Comments: 0

Q=∫_0 ^1 (((1−x^3 )(1−x^(33) )(1−x^(333) ))/(lnx))dx

$${Q}=\int_{\mathrm{0}} ^{\mathrm{1}} \frac{\left(\mathrm{1}−{x}^{\mathrm{3}} \right)\left(\mathrm{1}−{x}^{\mathrm{33}} \right)\left(\mathrm{1}−{x}^{\mathrm{333}} \right)}{{lnx}}{dx} \\ $$

Question Number 204979 Answers: 4 Comments: 0

factorizar x^4 + 1

$${factorizar} \\ $$$${x}^{\mathrm{4}} \:+\:\mathrm{1} \\ $$

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