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Question Number 194190 Answers: 0 Comments: 1

Explanation Why: While f(ax+b)+f(cx+d)=ex+g then f(x)=Ax^2 +Bx+C ¿

$${Explanation}\:{Why}: \\ $$$${While}\:{f}\left({ax}+{b}\right)+{f}\left({cx}+{d}\right)={ex}+{g} \\ $$$${then}\:{f}\left({x}\right)={Ax}^{\mathrm{2}} +{Bx}+{C}\:¿ \\ $$

Question Number 194185 Answers: 1 Comments: 0

lim_( x→ 0^( −) ) { (( x^( 2) +2cos(x) + ⌊−((tan(x))/x) ⌋)/(ax^( 4) )) } = 1 a = ? a: (1/(12)) b: −(1/2) c: 12 d: −12

$$ \\ $$$$\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\mathrm{lim}_{\:{x}\rightarrow\:\mathrm{0}^{\:−} } \:\left\{\:\frac{\:{x}^{\:\mathrm{2}} \:+\mathrm{2}{cos}\left({x}\right)\:+\:\lfloor−\frac{{tan}\left({x}\right)}{{x}}\:\rfloor}{{ax}^{\:\mathrm{4}} }\:\right\}\:=\:\mathrm{1}\:\:\:\:\:\:\:\:\:\:\:\: \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{a}\:=\:? \\ $$$$\:\:\:\:\:\:\:\:{a}:\:\:\:\frac{\mathrm{1}}{\mathrm{12}}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{b}:\:\:−\frac{\mathrm{1}}{\mathrm{2}}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{c}:\:\:\:\mathrm{12}\:\:\:\:\:\:\:\:\:\:\:\:\:\:{d}:\:\:−\mathrm{12}\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\: \\ $$

Question Number 194183 Answers: 1 Comments: 0

Σ_(n=1) ^∞ (1/(n(n+15)(n+30)))

$$\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\:\frac{\mathrm{1}}{{n}\left({n}+\mathrm{15}\right)\left({n}+\mathrm{30}\right)} \\ $$

Question Number 194176 Answers: 3 Comments: 0

Hello everyone I try to solve 4^(x+1) +2^(2−x) =65 Thx in advance

$${Hello}\:{everyone} \\ $$$${I}\:{try}\:{to}\:{solve}\:\mathrm{4}^{{x}+\mathrm{1}} +\mathrm{2}^{\mathrm{2}−{x}} =\mathrm{65} \\ $$$${Thx}\:{in}\:{advance} \\ $$

Question Number 194170 Answers: 0 Comments: 0

Question Number 194169 Answers: 0 Comments: 0

Question Number 194174 Answers: 1 Comments: 0

Know f(x^(−1) )=f^(−1) (x) (f^(−1) (x)=(1/(f(x)))) Find f(x)¿

$${Know}\:{f}\left({x}^{−\mathrm{1}} \right)={f}^{−\mathrm{1}} \left({x}\right)\:\left({f}^{−\mathrm{1}} \left({x}\right)=\frac{\mathrm{1}}{{f}\left({x}\right)}\right) \\ $$$${Find}\:{f}\left({x}\right)¿ \\ $$

Question Number 194166 Answers: 1 Comments: 0

Question Number 194172 Answers: 2 Comments: 1

Question Number 194165 Answers: 1 Comments: 0

Question Number 194163 Answers: 0 Comments: 0

Let a , b , c be positive real numbers prove that (a/b)+(b/c)+(c/a)+((3^3 (√(abc)))/(a+b+c))≥4

$$\boldsymbol{{Let}}\:\boldsymbol{{a}}\:,\:\boldsymbol{{b}}\:,\:\boldsymbol{{c}}\:\:\:\boldsymbol{{be}}\:\boldsymbol{{positive}}\:\boldsymbol{{real}}\:\boldsymbol{{numbers}} \\ $$$$\boldsymbol{{prove}}\:\boldsymbol{{that}} \\ $$$$\frac{\boldsymbol{{a}}}{\boldsymbol{{b}}}+\frac{\boldsymbol{{b}}}{\boldsymbol{{c}}}+\frac{\boldsymbol{{c}}}{\boldsymbol{{a}}}+\frac{\mathrm{3}^{\mathrm{3}} \sqrt{{abc}}}{\boldsymbol{{a}}+\boldsymbol{{b}}+\boldsymbol{{c}}}\geqslant\mathrm{4} \\ $$

Question Number 194159 Answers: 0 Comments: 0

...anybody tried question 193484? It′s not as hard as it may seem.

$$...\mathrm{anybody}\:\mathrm{tried}\:\mathrm{question}\:\mathrm{193484}? \\ $$$$\mathrm{It}'\mathrm{s}\:\mathrm{not}\:\mathrm{as}\:\mathrm{hard}\:\mathrm{as}\:\mathrm{it}\:\mathrm{may}\:\mathrm{seem}. \\ $$

Question Number 194158 Answers: 1 Comments: 0

Find all possible solutions: (1/s)+(1/t)+(1/u)+(1/v)=1 With s, t, u, v ∈N and s<t<u<v

$$\mathrm{Find}\:\mathrm{all}\:\mathrm{possible}\:\mathrm{solutions}: \\ $$$$\frac{\mathrm{1}}{{s}}+\frac{\mathrm{1}}{{t}}+\frac{\mathrm{1}}{{u}}+\frac{\mathrm{1}}{{v}}=\mathrm{1} \\ $$$$\mathrm{With}\:{s},\:{t},\:{u},\:{v}\:\in\mathbb{N}\:\mathrm{and}\:{s}<{t}<{u}<{v} \\ $$

Question Number 194147 Answers: 2 Comments: 0

lim_(n→+∞) ((1/1^2 )+(1/2^2 )+(1/3^2 )+...+(1/n^2 ))=?

$$\underset{\mathrm{n}\rightarrow+\infty} {\mathrm{lim}}\left(\frac{\mathrm{1}}{\mathrm{1}^{\mathrm{2}} }+\frac{\mathrm{1}}{\mathrm{2}^{\mathrm{2}} }+\frac{\mathrm{1}}{\mathrm{3}^{\mathrm{2}} }+...+\frac{\mathrm{1}}{\mathrm{n}^{\mathrm{2}} }\right)=? \\ $$

Question Number 194144 Answers: 5 Comments: 0

fill with different natural numbers: (1/(19))=(1/(( )))+(1/(( )))+(1/(( )))+(1/(( )))

$${fill}\:{with}\:{different}\:{natural}\:{numbers}: \\ $$$$\:\:\frac{\mathrm{1}}{\mathrm{19}}=\frac{\mathrm{1}}{\left(\:\:\right)}+\frac{\mathrm{1}}{\left(\:\:\right)}+\frac{\mathrm{1}}{\left(\:\:\right)}+\frac{\mathrm{1}}{\left(\:\:\right)} \\ $$

Question Number 194143 Answers: 0 Comments: 1

Question Number 194140 Answers: 1 Comments: 0

prove it : ((n),(k) )^( 2) ≥ ((( n)),((k−1)) ) × ((( n)),((k+1)) ) ; 1≤k≤n−1

$${prove}\:{it}\:: \\ $$$$\begin{pmatrix}{{n}}\\{{k}}\end{pmatrix}^{\:\mathrm{2}} \geqslant\:\begin{pmatrix}{\:\:\:\:{n}}\\{{k}−\mathrm{1}}\end{pmatrix}\:×\begin{pmatrix}{\:\:{n}}\\{{k}+\mathrm{1}}\end{pmatrix}\:\:\:\:\:;\:\:\:\mathrm{1}\leqslant{k}\leqslant{n}−\mathrm{1} \\ $$$$ \\ $$

Question Number 194139 Answers: 1 Comments: 1

Question Number 194135 Answers: 3 Comments: 0

determinant (((((23!−23)/(1.1!+2.2!+3.3!+...+21.21!)) =?)))

$$\:\:\:\:\:\:\begin{array}{|c|}{\frac{\mathrm{23}!−\mathrm{23}}{\mathrm{1}.\mathrm{1}!+\mathrm{2}.\mathrm{2}!+\mathrm{3}.\mathrm{3}!+...+\mathrm{21}.\mathrm{21}!}\:=?}\\\hline\end{array} \\ $$

Question Number 194131 Answers: 1 Comments: 1

Question Number 194128 Answers: 1 Comments: 0

Question Number 194127 Answers: 2 Comments: 0

Question Number 194116 Answers: 1 Comments: 0

Question Number 194113 Answers: 1 Comments: 0

Question Number 194105 Answers: 1 Comments: 0

x , y , z are positive real numbers if x^4 +y^4 +z^4 =1 Then find the minimum value of (x^3 /(1−x^8 ))+(y^3 /(1−y^8 ))+(z^3 /(1−z^8 ))

$$ \\ $$$${x}\:,\:{y}\:,\:{z}\:{are}\:{positive}\:{real}\:{numbers}\:{if}\:{x}^{\mathrm{4}} +{y}^{\mathrm{4}} +{z}^{\mathrm{4}} =\mathrm{1} \\ $$$${Then}\:{find}\:{the}\:{minimum}\:{value}\:{of}\: \\ $$$$\frac{{x}^{\mathrm{3}} }{\mathrm{1}−{x}^{\mathrm{8}} }+\frac{{y}^{\mathrm{3}} }{\mathrm{1}−{y}^{\mathrm{8}} }+\frac{{z}^{\mathrm{3}} }{\mathrm{1}−{z}^{\mathrm{8}} } \\ $$

Question Number 194089 Answers: 1 Comments: 3

Determiner le rayon r

$$\mathrm{Determiner}\:\mathrm{le}\:\mathrm{rayon}\:\boldsymbol{\mathrm{r}} \\ $$

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