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AllQuestion and Answers: Page 251

Question Number 195725 Answers: 0 Comments: 1

Question Number 195722 Answers: 0 Comments: 3

Question Number 195721 Answers: 1 Comments: 0

Question Number 195718 Answers: 1 Comments: 0

Question Number 195704 Answers: 1 Comments: 0

Question Number 195702 Answers: 1 Comments: 0

Question Number 195697 Answers: 1 Comments: 0

Question Number 195693 Answers: 2 Comments: 1

hello [Σ_(n=1) ^(10000) (1/( (√n)))]=? [ ] : is bracket thank you

$${hello} \\ $$$$\left[\underset{{n}=\mathrm{1}} {\overset{\mathrm{10000}} {\sum}}\frac{\mathrm{1}}{\:\sqrt{{n}}}\right]=? \\ $$$$\left[\:\right]\::\:{is}\:{bracket} \\ $$$${thank}\:{you} \\ $$$$ \\ $$

Question Number 195771 Answers: 2 Comments: 0

Question Number 195772 Answers: 2 Comments: 0

lim_(x→(π/3)) ((cos (((3x)/2))−sin (3x))/(sin (6x)))

$$\:\:\: \\ $$$$ \underset{{x}\rightarrow\frac{\pi}{\mathrm{3}}} {\mathrm{lim}}\:\frac{\mathrm{cos}\:\left(\frac{\mathrm{3}{x}}{\mathrm{2}}\right)−\mathrm{sin}\:\left(\mathrm{3}{x}\right)}{\mathrm{sin}\:\left(\mathrm{6}{x}\right)} \\ $$

Question Number 195746 Answers: 1 Comments: 0

Question Number 195674 Answers: 0 Comments: 4

∫_0 ^4 ((x!)/(5!(x−5)!)) dx = ???

$$\:\:\:\int_{\mathrm{0}} ^{\mathrm{4}} \:\frac{{x}!}{\mathrm{5}!\left({x}−\mathrm{5}\right)!}\:{dx}\:=\:??? \\ $$

Question Number 195666 Answers: 1 Comments: 2

sequence of string said to be orderly if element index i different to i+1 for example aba has orderly value 2 abab has orderly value 3 abaabb has orderly value 3 if there are 7 a and 13 b example aaaaaaabbbbbbbbbbbbb has orderly value 1 what is the mean of its orderly value for all possible sequences?

$$ \\ $$$$\:{sequence}\:{of}\:{string}\:{said}\:{to}\:{be}\:{orderly} \\ $$$$\:{if}\:{element}\:{index}\:{i}\:{different}\:{to}\:{i}+\mathrm{1} \\ $$$$\:{for}\:{example} \\ $$$$\:{aba}\:{has}\:{orderly}\:{value}\:\mathrm{2} \\ $$$$\:{abab}\:{has}\:{orderly}\:{value}\:\mathrm{3} \\ $$$$\:{abaabb}\:{has}\:{orderly}\:{value}\:\mathrm{3} \\ $$$$\:{if}\:{there}\:{are}\:\mathrm{7}\:{a}\:{and}\:\mathrm{13}\:{b} \\ $$$$\:{example} \\ $$$$\:{aaaaaaabbbbbbbbbbbbb}\:{has}\:{orderly}\:{value}\:\mathrm{1} \\ $$$$\:{what}\:{is}\:{the}\:{mean}\:{of}\:{its}\:{orderly}\:{value} \\ $$$$\:{for}\:{all}\:{possible}\:{sequences}? \\ $$$$ \\ $$

Question Number 195672 Answers: 2 Comments: 0

how many different words can be formed from the letters in aaacdefgbbbb such that a “a” and a “b” are not next to each other? (see also Q#195606)

$${how}\:{many}\:{different}\:{words}\:{can}\:{be} \\ $$$${formed}\:{from}\:{the}\:{letters}\:{in} \\ $$$$\boldsymbol{{aaacdefgbbbb}} \\ $$$${such}\:{that}\:{a}\:``\boldsymbol{{a}}''\:{and}\:{a}\:``\boldsymbol{{b}}''\:{are}\:{not} \\ $$$${next}\:{to}\:{each}\:{other}? \\ $$$$ \\ $$$$\left({see}\:{also}\:{Q}#\mathrm{195606}\right) \\ $$

Question Number 195680 Answers: 0 Comments: 0

Question Number 195653 Answers: 2 Comments: 0

_( →0) ( 1)^((√3)/ ) =?

$$\underset{ \rightarrow\mathrm{0}} { }\left( \mathrm{1}\right)^{\frac{\sqrt{\mathrm{3}}}{ }} \:=? \\ $$$$ \\ $$

Question Number 195652 Answers: 2 Comments: 0

e^(x+y) −e^(x−y) =1 then find (dy/dx)=?

$$ \\ $$$$\mathrm{e}^{\mathrm{x}+\mathrm{y}} −\mathrm{e}^{\mathrm{x}−\mathrm{y}} =\mathrm{1} \\ $$$$\mathrm{then}\:\mathrm{find}\:\:\:\frac{\mathrm{dy}}{\mathrm{dx}}=? \\ $$$$ \\ $$$$ \\ $$

Question Number 195651 Answers: 1 Comments: 0

0<x<1 (1/(1+x^1 ))+((2x)/(1+x^2 ))+((4x^3 )/(1+x^4 ))+((8x^7 )/(1+x^8 ))+((16x^(15) )/(1+x^(16) ))+....+∞ evaluate the previous summation

$$\mathrm{0}<{x}<\mathrm{1} \\ $$$$\frac{\mathrm{1}}{\mathrm{1}+{x}^{\mathrm{1}} }+\frac{\mathrm{2}{x}}{\mathrm{1}+{x}^{\mathrm{2}} }+\frac{\mathrm{4}{x}^{\mathrm{3}} }{\mathrm{1}+{x}^{\mathrm{4}} }+\frac{\mathrm{8}{x}^{\mathrm{7}} }{\mathrm{1}+{x}^{\mathrm{8}} }+\frac{\mathrm{16}{x}^{\mathrm{15}} }{\mathrm{1}+{x}^{\mathrm{16}} }+....+\infty \\ $$$${evaluate}\:{the}\:{previous}\:{summation} \\ $$

Question Number 195647 Answers: 1 Comments: 0

f(x)=((1276)/((x−1)^(ln(2/(4589))) )) domain f(x)=?

$${f}\left({x}\right)=\frac{\mathrm{1276}}{\left({x}−\mathrm{1}\right)^{{ln}\frac{\mathrm{2}}{\mathrm{4589}}} } \\ $$$${domain}\:{f}\left({x}\right)=? \\ $$

Question Number 195689 Answers: 0 Comments: 0

∫_1 ^3 f(x)^3 f′(x)dx=∫_1 ^3 (f(x)^3 )df(x)=∫_1 ^3 t^3 dt=(t^4 /4)∫_1 ^3 =((f(x)^4 )/4)∫_1 3

$$\int_{\mathrm{1}} ^{\mathrm{3}} {f}\left({x}\right)^{\mathrm{3}} {f}'\left({x}\right){dx}=\int_{\mathrm{1}} ^{\mathrm{3}} \left({f}\left({x}\right)^{\mathrm{3}} \right){df}\left({x}\right)=\int_{\mathrm{1}} ^{\mathrm{3}} {t}^{\mathrm{3}} {dt}=\frac{{t}^{\mathrm{4}} }{\mathrm{4}}\int_{\mathrm{1}} ^{\mathrm{3}} =\frac{{f}\left({x}\right)^{\mathrm{4}} }{\mathrm{4}}\int_{\mathrm{1}} \mathrm{3} \\ $$

Question Number 195688 Answers: 1 Comments: 0

Question Number 195681 Answers: 2 Comments: 0

Question Number 195628 Answers: 2 Comments: 3

an unsolved old question #190875 a, b, c are real roots of the equation x^3 −7x^2 +4x+1=0. find (1/( (a)^(1/3) ))+(1/( (b)^(1/3) ))+(1/( (c)^(1/3) ))=?

$$\underline{{an}\:{unsolved}\:{old}\:{question}\:#\mathrm{190875}} \\ $$$${a},\:{b},\:{c}\:{are}\:{real}\:{roots}\:{of}\:{the}\:{equation} \\ $$$${x}^{\mathrm{3}} −\mathrm{7}{x}^{\mathrm{2}} +\mathrm{4}{x}+\mathrm{1}=\mathrm{0}. \\ $$$${find}\:\frac{\mathrm{1}}{\:\sqrt[{\mathrm{3}}]{{a}}}+\frac{\mathrm{1}}{\:\sqrt[{\mathrm{3}}]{{b}}}+\frac{\mathrm{1}}{\:\sqrt[{\mathrm{3}}]{{c}}}=? \\ $$

Question Number 195708 Answers: 2 Comments: 0

Prove that : log_(((√a) − b)) ((√a) +b) = −1

$$\boldsymbol{{Prove}}\:\boldsymbol{{that}}\::\:\boldsymbol{{log}}_{\left(\sqrt{\boldsymbol{{a}}}\:−\:\boldsymbol{{b}}\right)} \left(\sqrt{\boldsymbol{{a}}}\:+\boldsymbol{{b}}\right)\:=\:−\mathrm{1} \\ $$

Question Number 195707 Answers: 1 Comments: 0

Question Number 195619 Answers: 2 Comments: 0

lim_(x→0) (( ((1+ ))^(1/3) )/ )

$$\:\: \\ $$$$ \underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{ \sqrt[{\mathrm{3}}]{\mathrm{1}+ }\: }{ } \\ $$

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