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AllQuestion and Answers: Page 204

Question Number 194488 Answers: 0 Comments: 0

Question Number 194482 Answers: 1 Comments: 0

determinant ((( ⋐)))

$$\:\:\:\:\:\begin{array}{|c|}{\:\cancel{\underline{\underbrace{\Subset}}}}\\\hline\end{array} \\ $$

Question Number 194475 Answers: 2 Comments: 2

How many sets of two factors of 720 are coprime to each other? (A) 63 (B) 64 (C) 65 (D) 67

$$\mathrm{How}\:\mathrm{many}\:\mathrm{sets}\:\mathrm{of}\:\mathrm{two}\:\mathrm{factors}\:\mathrm{of}\:\mathrm{720}\:\mathrm{are}\: \\ $$$$\mathrm{coprime}\:\mathrm{to}\:\mathrm{each}\:\mathrm{other}? \\ $$$$\left(\mathrm{A}\right)\:\mathrm{63}\:\:\:\:\left(\mathrm{B}\right)\:\mathrm{64}\:\:\:\:\:\left(\mathrm{C}\right)\:\mathrm{65}\:\:\:\:\:\:\:\:\:\left(\mathrm{D}\right)\:\mathrm{67} \\ $$$$ \\ $$

Question Number 194467 Answers: 2 Comments: 0

⇊

$$\:\:\:\underline{\downdownarrows} \\ $$

Question Number 194466 Answers: 2 Comments: 0

⋐

$$\:\:\:\:\Subset \\ $$

Question Number 194464 Answers: 1 Comments: 0

Question Number 194463 Answers: 1 Comments: 0

Question Number 194462 Answers: 1 Comments: 0

Prove that ∫^( +∞^ ) _( 0) ((1−e^(−x^2 ) )/x^2 )dx=(√𝛑)

$$\mathrm{Prove}\:\mathrm{that}\:\:\:\:\:\:\:\:\underset{\:\mathrm{0}} {\int}^{\:+\infty^{} } \frac{\mathrm{1}−\boldsymbol{{e}}^{−\boldsymbol{{x}}^{\mathrm{2}} } }{\boldsymbol{{x}}^{\mathrm{2}} }\boldsymbol{{dx}}=\sqrt{\boldsymbol{\pi}} \\ $$

Question Number 194456 Answers: 2 Comments: 0

$$\:\:\:\:\:\:\cancel{ } \\ $$

Question Number 194455 Answers: 1 Comments: 0

Question Number 194451 Answers: 1 Comments: 0

⊪

$$\:\:\:\:\:\:\cancel{\underline{\underbrace{\Vvdash}}} \\ $$

Question Number 194448 Answers: 0 Comments: 0

If a , b , c >0 , such that a+b+c=3 prove that (1/(1+ab))+(1/(1+ac))+(1/(1+bc))≥(9/(2((√a)+(√b)+(√c))))

$${If}\:{a}\:,\:{b}\:,\:{c}\:>\mathrm{0}\:,\:{such}\:{that}\:{a}+{b}+{c}=\mathrm{3} \\ $$$${prove}\:{that} \\ $$$$\frac{\mathrm{1}}{\mathrm{1}+{ab}}+\frac{\mathrm{1}}{\mathrm{1}+{ac}}+\frac{\mathrm{1}}{\mathrm{1}+{bc}}\geqslant\frac{\mathrm{9}}{\mathrm{2}\left(\sqrt{{a}}+\sqrt{{b}}+\sqrt{{c}}\right)} \\ $$

Question Number 194446 Answers: 0 Comments: 0

Question Number 194445 Answers: 1 Comments: 0

Σ_(n=1) ^∞ (1/(n^2 (n+a)))=¿ (a≠0)

$$\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\:\frac{\mathrm{1}}{{n}^{\mathrm{2}} \left({n}+{a}\right)}=¿ \\ $$$$\left({a}\neq\mathrm{0}\right) \\ $$

Question Number 194444 Answers: 1 Comments: 0

Question Number 194436 Answers: 1 Comments: 0

Question Number 194434 Answers: 1 Comments: 0

calcul e^(2ln(1+u) ) −e^(−2ln(1+u)) =?

$${calcul} \\ $$$${e}^{\mathrm{2}{ln}\left(\mathrm{1}+{u}\right)\:} −{e}^{−\mathrm{2}{ln}\left(\mathrm{1}+{u}\right)} \:=? \\ $$

Question Number 194431 Answers: 0 Comments: 0

Question Number 194426 Answers: 0 Comments: 0

Question Number 194425 Answers: 1 Comments: 0

$$\:\:\:\:\:\:\:\underbrace{ } \\ $$

Question Number 194422 Answers: 1 Comments: 0

What books use for studying inequalities for beginners

$${What}\:{books}\:{use}\:{for}\:{studying}\:{inequalities} \\ $$$${for}\:{beginners}\: \\ $$

Question Number 194421 Answers: 0 Comments: 1

If a , b , c >0 , such that a+b+c=3 prove that (1/(1+ab))+(1/(1+ac))+(1/(1+bc))≥(9/(2((√a)+(√b)+(√c))))

$$ \\ $$$${If}\:{a}\:,\:{b}\:,\:{c}\:>\mathrm{0}\:,\:{such}\:{that}\:{a}+{b}+{c}=\mathrm{3} \\ $$$${prove}\:{that} \\ $$$$\frac{\mathrm{1}}{\mathrm{1}+{ab}}+\frac{\mathrm{1}}{\mathrm{1}+{ac}}+\frac{\mathrm{1}}{\mathrm{1}+{bc}}\geqslant\frac{\mathrm{9}}{\mathrm{2}\left(\sqrt{{a}}+\sqrt{{b}}+\sqrt{{c}}\right)} \\ $$

Question Number 198279 Answers: 1 Comments: 0

if f(x) is also differentiable on R such that f′(x) > f(x) ∀ x ∈ R and f(x_0 ) = 0 then prove that f(x) ≥ 0 ∀ x > x_0

$$\:\:\mathrm{if}\:\mathrm{f}\left(\mathrm{x}\right)\:\mathrm{is}\:\mathrm{also}\:\mathrm{differentiable}\:\mathrm{on}\:\mathbb{R}\:\mathrm{such}\:\mathrm{that} \\ $$$$\:\:\mathrm{f}'\left(\mathrm{x}\right)\:>\:\mathrm{f}\left(\mathrm{x}\right)\:\forall\:\mathrm{x}\:\in\:\mathbb{R}\:{and}\:\mathrm{f}\left(\mathrm{x}_{\mathrm{0}} \right)\:=\:\mathrm{0}\:\mathrm{then}\: \\ $$$$\:\:\mathrm{prove}\:\mathrm{that}\:\:\mathrm{f}\left(\mathrm{x}\right)\:\geqslant\:\mathrm{0}\:\forall\:\mathrm{x}\:>\:\mathrm{x}_{\mathrm{0}} \\ $$

Question Number 194412 Answers: 1 Comments: 0

Question Number 194410 Answers: 0 Comments: 1

Question Number 194406 Answers: 2 Comments: 0

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