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Question Number 211859 Answers: 0 Comments: 0

Question Number 211857 Answers: 1 Comments: 0

∫_1 ^∞ (((tan^(−1) x)/x)×((ln x)/x))dx=?

$$\underset{\mathrm{1}} {\overset{\infty} {\int}}\left(\frac{\mathrm{tan}^{−\mathrm{1}} \:{x}}{{x}}×\frac{\mathrm{ln}\:{x}}{{x}}\right){dx}=? \\ $$

Question Number 211851 Answers: 0 Comments: 1

Question Number 211849 Answers: 1 Comments: 1

Question Number 211845 Answers: 1 Comments: 0

Question Number 211828 Answers: 1 Comments: 0

Question Number 211822 Answers: 1 Comments: 1

Question Number 211820 Answers: 2 Comments: 2

Question Number 211819 Answers: 2 Comments: 0

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Question Number 211817 Answers: 1 Comments: 0

Question Number 211815 Answers: 1 Comments: 0

ax^2 +bx+c=0 has roots α and β and (α/β)=(λ/μ). show that λμb^2 = ac(λ+μ)^2

$${ax}^{\mathrm{2}} +{bx}+{c}=\mathrm{0}\:{has}\:{roots}\:\alpha\:{and}\:\beta \\ $$$${and}\:\frac{\alpha}{\beta}=\frac{\lambda}{\mu}.\:{show}\:{that}\:\lambda\mu{b}^{\mathrm{2}} \:=\:{ac}\left(\lambda+\mu\right)^{\mathrm{2}} \\ $$

Question Number 211837 Answers: 0 Comments: 0

Question Number 211791 Answers: 1 Comments: 0

can someone please tell me the difference b/w (=) and (::=) I searched up and showed it was related to assertion,definition,propert def....i don′t know. please help

$$\mathrm{can}\:\mathrm{someone}\:\mathrm{please}\:\mathrm{tell}\:\mathrm{me}\:\mathrm{the}\:\mathrm{difference}\:\mathrm{b}/\mathrm{w}\:\left(=\right)\:\mathrm{and}\:\left(::=\right) \\ $$$$ \\ $$$$\mathrm{I}\:\mathrm{searched}\:\mathrm{up}\:\mathrm{and}\:\mathrm{showed}\:\mathrm{it}\:\mathrm{was}\:\mathrm{related}\:\mathrm{to}\:\mathrm{assertion},\mathrm{definition},\mathrm{propert}\:\mathrm{def}....\mathrm{i}\:\mathrm{don}'\mathrm{t}\:\mathrm{know}.\:\mathrm{please}\:\mathrm{help} \\ $$

Question Number 211787 Answers: 0 Comments: 0

Compare: 5^(100) , 6^(91) , 7^(90) , 8^(85)

$$\mathrm{Compare}: \\ $$$$ \\ $$$$\mathrm{5}^{\mathrm{100}} \:,\:\mathrm{6}^{\mathrm{91}} \:,\:\mathrm{7}^{\mathrm{90}} \:,\:\mathrm{8}^{\mathrm{85}} \\ $$

Question Number 211788 Answers: 0 Comments: 0

Question Number 211793 Answers: 0 Comments: 0

Question Number 211796 Answers: 1 Comments: 0

Question Number 211795 Answers: 0 Comments: 0

Question Number 211798 Answers: 1 Comments: 0

Question Number 211797 Answers: 4 Comments: 0

Question Number 211778 Answers: 1 Comments: 1

Show that: ∫_0 ^( (𝛑/4)) sin^4 x 2x dx = ((3π −4)/(192))

$$\:\:\mathrm{Show}\:\mathrm{that}: \\ $$$$\:\int_{\mathrm{0}} ^{\:\frac{\boldsymbol{\pi}}{\mathrm{4}}} \:\boldsymbol{\mathrm{sin}}^{\mathrm{4}} \boldsymbol{\mathrm{x}}\:\mathrm{2}\boldsymbol{\mathrm{x}}\:\boldsymbol{\mathrm{dx}}\:=\:\frac{\mathrm{3}\pi\:−\mathrm{4}}{\mathrm{192}} \\ $$

Question Number 211761 Answers: 2 Comments: 0

If x = ((4a^2 b)/(4b^2 + 1)) where b > (1/2) then (((√(a^2 + x)) + (√(a^2 − x)))/( (√(a^2 + x)) − (√(a^2 − x)))) = ?

$$\mathrm{If}\:{x}\:=\:\frac{\mathrm{4}{a}^{\mathrm{2}} {b}}{\mathrm{4}{b}^{\mathrm{2}} \:+\:\mathrm{1}}\:\mathrm{where}\:{b}\:>\:\frac{\mathrm{1}}{\mathrm{2}}\:\mathrm{then} \\ $$$$\frac{\sqrt{{a}^{\mathrm{2}} \:+\:{x}}\:+\:\sqrt{{a}^{\mathrm{2}} \:−\:{x}}}{\:\sqrt{{a}^{\mathrm{2}} \:+\:{x}}\:−\:\sqrt{{a}^{\mathrm{2}} \:−\:{x}}}\:=\:? \\ $$

Question Number 211759 Answers: 4 Comments: 1

lim_(x→0) ((e^(sin x) −e^x )/(sin x−x))=?

$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{{e}^{\mathrm{sin}\:{x}} −{e}^{{x}} }{\mathrm{sin}\:{x}−{x}}=? \\ $$

Question Number 211753 Answers: 1 Comments: 0

find all (n,m) such that ((n^2 −m)/(m^2 −n)) ∈ Z

$${find}\:{all}\:\left({n},{m}\right)\:{such}\:{that}\:\frac{{n}^{\mathrm{2}} −{m}}{{m}^{\mathrm{2}} −{n}}\:\in\:\mathbb{Z} \\ $$

Question Number 211750 Answers: 1 Comments: 0

lim_(x→∞) (((a^(1/x) +b^(1/x) )/2))^x ;(a,b)∈R_+ ^∗

$$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\left(\frac{{a}^{\mathrm{1}/{x}} +{b}^{\mathrm{1}/{x}} }{\mathrm{2}}\right)^{{x}} ;\left({a},{b}\right)\in\mathbb{R}_{+} ^{\ast} \\ $$

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