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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

Question Number 194401 Answers: 0 Comments: 0

Hi Please do not post junk content in this forum. It does not help you in anyway and it increases our effort in cleaning up.

$$\mathrm{Hi} \\ $$$$\mathrm{Please}\:\mathrm{do}\:\mathrm{not}\:\mathrm{post}\:\mathrm{junk}\:\mathrm{content}\:\mathrm{in} \\ $$$$\mathrm{this}\:\mathrm{forum}.\:\mathrm{It}\:\mathrm{does}\:\mathrm{not}\:\mathrm{help}\:\mathrm{you}\:\mathrm{in} \\ $$$$\mathrm{anyway}\:\mathrm{and}\:\mathrm{it}\:\mathrm{increases}\:\mathrm{our}\:\mathrm{effort}\: \\ $$$$\mathrm{in}\:\mathrm{cleaning}\:\mathrm{up}. \\ $$

Question Number 194389 Answers: 1 Comments: 0

(√(√(49+20(√6))))=?

$$\sqrt{\sqrt{\mathrm{49}+\mathrm{20}\sqrt{\mathrm{6}}}}=? \\ $$

Question Number 194388 Answers: 0 Comments: 0

∫(((1+x^2 )sin x+4cos x)/(2(1+x^2 )^3 )) dx

$$\int\frac{\left(\mathrm{1}+{x}^{\mathrm{2}} \right)\mathrm{sin}\:{x}+\mathrm{4cos}\:{x}}{\mathrm{2}\left(\mathrm{1}+{x}^{\mathrm{2}} \right)^{\mathrm{3}} }\:{dx} \\ $$

Question Number 194386 Answers: 1 Comments: 0

calcul the the derive of cos^3 ((θ/3))′

$${calcul}\:{the}\:{the}\:{derive}\:{of} \\ $$$${cos}^{\mathrm{3}} \left(\frac{\theta}{\mathrm{3}}\right)' \\ $$

Question Number 194384 Answers: 0 Comments: 1

Question Number 194383 Answers: 0 Comments: 0

Question Number 194373 Answers: 0 Comments: 0

Show Σ_(i=1) ^n ((1/(2i−1))− (1/(2i)))=Σ_(i=1) ^n (1/(n+i))

$${Show}\:\:\: \\ $$$$\underset{{i}=\mathrm{1}} {\overset{{n}} {\sum}}\left(\frac{\mathrm{1}}{\mathrm{2}{i}−\mathrm{1}}−\:\frac{\mathrm{1}}{\mathrm{2}{i}}\right)=\underset{{i}=\mathrm{1}} {\overset{{n}} {\sum}}\:\frac{\mathrm{1}}{{n}+{i}}\: \\ $$$$ \\ $$

Question Number 194363 Answers: 1 Comments: 1

Question Number 194359 Answers: 1 Comments: 1

v2.282 has been published. This update fixes issues with missed notifications and adds an arbitarary precision scientific calculator.

$${v}\mathrm{2}.\mathrm{282}\:\mathrm{has}\:\mathrm{been}\:\mathrm{published}.\:\mathrm{This} \\ $$$$\mathrm{update}\:\mathrm{fixes}\:\mathrm{issues}\:\mathrm{with}\:\mathrm{missed} \\ $$$$\mathrm{notifications}\:\mathrm{and}\:\mathrm{adds}\:\mathrm{an} \\ $$$$\mathrm{arbitarary}\:\mathrm{precision}\: \\ $$$$\mathrm{scientific}\:\mathrm{calculator}. \\ $$

Question Number 194352 Answers: 0 Comments: 0

⋐

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

Question Number 194350 Answers: 2 Comments: 0

Question Number 194344 Answers: 2 Comments: 0

Question Number 194343 Answers: 3 Comments: 0

⌊9.9^− ⌋ = ?

$$\lfloor\mathrm{9}.\overset{−} {\mathrm{9}}\rfloor\:=\:? \\ $$

Question Number 194338 Answers: 2 Comments: 0

Question Number 194335 Answers: 1 Comments: 0

Question Number 194334 Answers: 0 Comments: 2

^()

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

Question Number 194331 Answers: 1 Comments: 0

Question Number 194327 Answers: 1 Comments: 0

If ta4θ = 1, find the values of θ.

$$\mathrm{If}\:\mathrm{ta4}\theta\:=\:\mathrm{1},\:\mathrm{find}\:\mathrm{the}\:\mathrm{values}\:\mathrm{of}\:\theta. \\ $$

Question Number 194326 Answers: 1 Comments: 0

(√(((√(x^2 +66^2 +x))/x) )) −(√(x(√(x^2 +66^2 ))−x^2 )) = 5

$$\:\:\sqrt{\frac{\sqrt{\mathrm{x}^{\mathrm{2}} +\mathrm{66}^{\mathrm{2}} +\mathrm{x}}}{\mathrm{x}}\:}\:−\sqrt{\mathrm{x}\sqrt{\mathrm{x}^{\mathrm{2}} +\mathrm{66}^{\mathrm{2}} }−\mathrm{x}^{\mathrm{2}} }\:=\:\mathrm{5}\: \\ $$

Question Number 194325 Answers: 1 Comments: 0

$$\:\:\cancel{\mathcal{X}} \\ $$

Question Number 194322 Answers: 0 Comments: 0

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