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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

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

Question Number 204978 Answers: 1 Comments: 0

Question Number 204970 Answers: 1 Comments: 1

Question Number 204961 Answers: 2 Comments: 0

∫ (1/(1+cot 3x)) dx =

$$\int\:\frac{\mathrm{1}}{\mathrm{1}+\mathrm{cot}\:\mathrm{3}{x}}\:{dx}\:=\:\: \\ $$

Question Number 204957 Answers: 2 Comments: 0

2×2 matrix A and B satisfy that AB+A=BA+B. Prove that (A−B)^2 =O.

$$\mathrm{2}×\mathrm{2}\:\mathrm{matrix}\:\boldsymbol{\mathrm{A}}\:\mathrm{and}\:\boldsymbol{\mathrm{B}}\:\mathrm{satisfy}\:\mathrm{that} \\ $$$$\boldsymbol{\mathrm{AB}}+\boldsymbol{\mathrm{A}}=\boldsymbol{\mathrm{BA}}+\boldsymbol{\mathrm{B}}. \\ $$$$\mathrm{Prove}\:\mathrm{that}\:\left(\boldsymbol{\mathrm{A}}−\boldsymbol{\mathrm{B}}\right)^{\mathrm{2}} =\boldsymbol{\mathrm{O}}. \\ $$

Question Number 204948 Answers: 0 Comments: 4

prove a^2 +b^2 +c^2 +((abc))^(1/3) ≥4 if ab+bc+ac=3

$${prove}\: \\ $$$${a}^{\mathrm{2}} +{b}^{\mathrm{2}} +{c}^{\mathrm{2}} +\sqrt[{\mathrm{3}}]{{abc}}\geqslant\mathrm{4} \\ $$$${if} \\ $$$${ab}+{bc}+{ac}=\mathrm{3} \\ $$

Question Number 204947 Answers: 1 Comments: 0

f′(x)+4x−6x.e^(x^2 −f(x)−1) =0 f(x)=¿

$${f}'\left({x}\right)+\mathrm{4}{x}−\mathrm{6}{x}.{e}^{{x}^{\mathrm{2}} −{f}\left({x}\right)−\mathrm{1}} =\mathrm{0} \\ $$$${f}\left({x}\right)=¿ \\ $$

Question Number 204944 Answers: 1 Comments: 1

Question Number 204941 Answers: 0 Comments: 0

Question Number 205204 Answers: 1 Comments: 0

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