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AllQuestion and Answers: Page 587

Question Number 159233 Answers: 1 Comments: 0

Question Number 159229 Answers: 2 Comments: 0

lim_(x→∞) x((√(x^2 +2x))+x−2(√(x^2 +x)) )=?

$$\:\:\:\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:{x}\left(\sqrt{{x}^{\mathrm{2}} +\mathrm{2}{x}}+{x}−\mathrm{2}\sqrt{{x}^{\mathrm{2}} +{x}}\:\right)=? \\ $$

Question Number 159226 Answers: 1 Comments: 0

Ω = ∫_0 ^∞ (((x^5 )^(1/6) −(√x))/((1+x^2 ) ln x)) dx =?

$$\:\Omega\:=\:\int_{\mathrm{0}} ^{\infty} \frac{\sqrt[{\mathrm{6}}]{{x}^{\mathrm{5}} }−\sqrt{{x}}}{\left(\mathrm{1}+{x}^{\mathrm{2}} \right)\:\mathrm{ln}\:{x}}\:{dx}\:=? \\ $$

Question Number 159222 Answers: 1 Comments: 1

find an explicit formula for the sequence (2/3), (4/5), (8/9), ((16)/(17)), ((32)/(33)), ...

$$\mathrm{find}\:\mathrm{an}\:\mathrm{explicit}\:\mathrm{formula}\:\mathrm{for} \\ $$$$\mathrm{the}\:\mathrm{sequence} \\ $$$$\frac{\mathrm{2}}{\mathrm{3}},\:\frac{\mathrm{4}}{\mathrm{5}},\:\frac{\mathrm{8}}{\mathrm{9}},\:\frac{\mathrm{16}}{\mathrm{17}},\:\frac{\mathrm{32}}{\mathrm{33}},\:... \\ $$

Question Number 159221 Answers: 2 Comments: 4

find the general term of the sequence 3, 5 , 9, 17, 33, ...

$$\mathrm{find}\:\mathrm{the}\:\mathrm{general}\:\mathrm{term}\:\mathrm{of} \\ $$$$\mathrm{the}\:\mathrm{sequence}\: \\ $$$$\mathrm{3},\:\mathrm{5}\:,\:\mathrm{9},\:\mathrm{17},\:\mathrm{33},\:... \\ $$

Question Number 159217 Answers: 1 Comments: 0

Question Number 159189 Answers: 1 Comments: 0

Question Number 159188 Answers: 3 Comments: 2

If α and β are the roots of equation (√(t/(1−t))) + (√((1−t)/t)) = ((13)/6) . Find 2α+3β .

$$\:{If}\:\alpha\:{and}\:\beta\:{are}\:{the}\:{roots}\:{of} \\ $$$${equation}\:\sqrt{\frac{{t}}{\mathrm{1}−{t}}}\:+\:\sqrt{\frac{\mathrm{1}−{t}}{{t}}}\:=\:\frac{\mathrm{13}}{\mathrm{6}}\:. \\ $$$${Find}\:\mathrm{2}\alpha+\mathrm{3}\beta\:. \\ $$

Question Number 159180 Answers: 1 Comments: 0

Question Number 159179 Answers: 1 Comments: 0

X^3 −4X^2 −6X−24 = 0

$$\:\:\mathcal{X}^{\mathrm{3}} −\mathrm{4}\mathcal{X}^{\mathrm{2}} −\mathrm{6}\mathcal{X}−\mathrm{24}\:=\:\mathrm{0} \\ $$

Question Number 159173 Answers: 1 Comments: 0

Question Number 159172 Answers: 1 Comments: 0

Question Number 159171 Answers: 1 Comments: 0

Prove by absurd that log 2 is the number irrational

$${Prove}\:{by}\:{absurd}\:{that}\:\mathrm{log}\:\mathrm{2}\:{is}\:{the} \\ $$$${number}\:{irrational} \\ $$

Question Number 159170 Answers: 1 Comments: 1

Question Number 159300 Answers: 1 Comments: 0

Question Number 159163 Answers: 2 Comments: 1

Question Number 159159 Answers: 1 Comments: 0

Three students are runing for school SRC president, kada′s probability of winning is (1/8), Atiga′s probability of winnig (1/3) and kada is half as likely to win as Apio. i. what is the probability that both Atiga and Apio draw ii. what is the probability that only one wins the presidency.

$$\:\mathrm{Three}\:\mathrm{students}\:\mathrm{are}\:\mathrm{runing}\:\mathrm{for}\:\mathrm{school} \\ $$$$\:\mathrm{SRC}\:\mathrm{president},\:\mathrm{kada}'\mathrm{s}\:\mathrm{probability}\:\mathrm{of} \\ $$$$\mathrm{winning}\:\mathrm{is}\:\frac{\mathrm{1}}{\mathrm{8}},\:\mathrm{Atiga}'\mathrm{s}\:\mathrm{probability}\: \\ $$$$\mathrm{of}\:\mathrm{winnig}\:\frac{\mathrm{1}}{\mathrm{3}}\:\mathrm{and}\:\mathrm{kada}\:\mathrm{is}\:\mathrm{half}\:\mathrm{as}\:\mathrm{likely} \\ $$$$\mathrm{to}\:\mathrm{win}\:\mathrm{as}\:\mathrm{Apio}.\: \\ $$$$\mathrm{i}.\:\mathrm{what}\:\mathrm{is}\:\mathrm{the}\:\mathrm{probability}\:\mathrm{that}\:\mathrm{both}\: \\ $$$$\:\mathrm{Atiga}\:\mathrm{and}\:\mathrm{Apio}\:\mathrm{draw} \\ $$$$\mathrm{ii}.\:\mathrm{what}\:\mathrm{is}\:\mathrm{the}\:\mathrm{probability}\:\mathrm{that}\:\mathrm{only} \\ $$$$\mathrm{one}\:\mathrm{wins}\:\mathrm{the}\:\mathrm{presidency}. \\ $$

Question Number 159292 Answers: 1 Comments: 0

Find: 𝛀 =∫_( 0) ^( ∞) ((x arctan(x))/((x + 1)(x^2 + 1))) dx

$$\mathrm{Find}:\:\:\boldsymbol{\Omega}\:=\underset{\:\mathrm{0}} {\overset{\:\infty} {\int}}\frac{\mathrm{x}\:\mathrm{arctan}\left(\mathrm{x}\right)}{\left(\mathrm{x}\:+\:\mathrm{1}\right)\left(\mathrm{x}^{\mathrm{2}} \:+\:\mathrm{1}\right)}\:\mathrm{dx} \\ $$$$ \\ $$

Question Number 159157 Answers: 1 Comments: 0

Question Number 159184 Answers: 0 Comments: 2

Question Number 159153 Answers: 0 Comments: 0

Question Number 159152 Answers: 1 Comments: 0

Question Number 159146 Answers: 0 Comments: 0

Find the absolute extrema of f(x)= 2 csc x + cot x on the interval ((π/2), ((3π)/2) ]

$${Find}\:{the}\:{absolute}\:{extrema}\:{of} \\ $$$${f}\left({x}\right)=\:\mathrm{2}\:\mathrm{csc}\:{x}\:+\:\mathrm{cot}\:{x}\:{on}\:{the}\: \\ $$$${interval}\:\left(\frac{\pi}{\mathrm{2}},\:\frac{\mathrm{3}\pi}{\mathrm{2}}\:\right] \\ $$

Question Number 159143 Answers: 1 Comments: 0

Question Number 159142 Answers: 2 Comments: 1

lim_(x→−(π/4)) (((π/( (√8))) −(√2) x. tan x)/(sin x+cos x)) =?

$$\:\underset{{x}\rightarrow−\frac{\pi}{\mathrm{4}}} {\mathrm{lim}}\:\frac{\frac{\pi}{\:\sqrt{\mathrm{8}}}\:−\sqrt{\mathrm{2}}\:{x}.\:\mathrm{tan}\:{x}}{\mathrm{sin}\:{x}+\mathrm{cos}\:{x}}\:=? \\ $$

Question Number 159137 Answers: 1 Comments: 4

Yesterday,Mr John earned $50 mowing lawns, today Mr. John earned 60percent of what he earned yesterday mowing lawns. how much money did Mr Jacob earned mowing lawns today??

$$\mathrm{Yesterday},\mathrm{Mr}\:\mathrm{John}\:\mathrm{earned}\:\$\mathrm{50} \\ $$$$\mathrm{mowing}\:\mathrm{lawns},\:\mathrm{today}\:\mathrm{Mr}.\:\mathrm{John} \\ $$$$\mathrm{earned}\:\mathrm{60percent}\:\mathrm{of}\:\mathrm{what}\:\mathrm{he}\:\mathrm{earned} \\ $$$$\mathrm{yesterday}\:\mathrm{mowing}\:\mathrm{lawns}.\:\mathrm{how} \\ $$$$\mathrm{much}\:\mathrm{money}\:\mathrm{did}\:\mathrm{Mr}\:\mathrm{Jacob}\:\mathrm{earned} \\ $$$$\mathrm{mowing}\:\mathrm{lawns}\:\mathrm{today}?? \\ $$

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