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Question Number 161202 Answers: 0 Comments: 0

lim_(n→∞) Σ_(k=1) ^n ((k/n))^n =?

$$\underset{\mathrm{n}\rightarrow\infty} {\mathrm{lim}}\underset{\mathrm{k}=\mathrm{1}} {\overset{\mathrm{n}} {\sum}}\left(\frac{\mathrm{k}}{\mathrm{n}}\right)^{\mathrm{n}} =? \\ $$

Question Number 161196 Answers: 0 Comments: 0

Montrons que B_2 (0, 1) est homeomorphe a^ R^2 . Ou^ B_2 (0, 1)=boule unite^ de R^2 .

$$\mathrm{Montrons}\:\mathrm{que}\:\mathrm{B}_{\mathrm{2}} \left(\mathrm{0},\:\mathrm{1}\right)\:\mathrm{est}\:\mathrm{homeomorphe}\:\grave {\mathrm{a}}\:\mathbb{R}^{\mathrm{2}} . \\ $$$$\mathrm{O}\grave {\mathrm{u}}\:\mathrm{B}_{\mathrm{2}} \left(\mathrm{0},\:\mathrm{1}\right)=\mathrm{boule}\:\mathrm{unit}\acute {\mathrm{e}}\:\mathrm{de}\:\mathbb{R}^{\mathrm{2}} . \\ $$

Question Number 161194 Answers: 0 Comments: 1

TAKEN FROM REAL LIFE if I try to walk into a shop through a super clean closed glass door and get myself a bloody nose then what′s the value of the brake acceleration when we assume 1) my walking speed is 7km/hr 2) the crumple zone of my nose is 1/2′′ 3) the brake acceleration is constant

$$\mathbb{TAKEN}\:\mathbb{FROM}\:\mathbb{REAL}\:\mathbb{LIFE} \\ $$$$\mathrm{if}\:\mathrm{I}\:\mathrm{try}\:\mathrm{to}\:\mathrm{walk}\:\mathrm{into}\:\mathrm{a}\:\mathrm{shop}\:\mathrm{through}\:\mathrm{a}\:\mathrm{super} \\ $$$$\mathrm{clean}\:\mathrm{closed}\:\mathrm{glass}\:\mathrm{door}\:\mathrm{and}\:\mathrm{get}\:\mathrm{myself}\:\mathrm{a} \\ $$$$\mathrm{bloody}\:\mathrm{nose}\:\mathrm{then}\:\mathrm{what}'\mathrm{s}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{the} \\ $$$$\mathrm{brake}\:\mathrm{acceleration}\:\mathrm{when}\:\mathrm{we}\:\mathrm{assume} \\ $$$$\left.\mathrm{1}\right)\:\mathrm{my}\:\mathrm{walking}\:\mathrm{speed}\:\mathrm{is}\:\mathrm{7km}/\mathrm{hr} \\ $$$$\left.\mathrm{2}\right)\:\mathrm{the}\:\mathrm{crumple}\:\mathrm{zone}\:\mathrm{of}\:\mathrm{my}\:\mathrm{nose}\:\mathrm{is}\:\mathrm{1}/\mathrm{2}'' \\ $$$$\left.\mathrm{3}\right)\:\mathrm{the}\:\mathrm{brake}\:\mathrm{acceleration}\:\mathrm{is}\:\mathrm{constant} \\ $$

Question Number 161192 Answers: 0 Comments: 2

Question Number 161186 Answers: 2 Comments: 0

Question Number 161181 Answers: 0 Comments: 1

x=cot^(−1) ((√(cos θ)))−tan^(−1) ((√(cos θ))) sin x=?

$$\:\:{x}=\mathrm{cot}^{−\mathrm{1}} \left(\sqrt{\mathrm{cos}\:\theta}\right)−\mathrm{tan}^{−\mathrm{1}} \left(\sqrt{\mathrm{cos}\:\theta}\right) \\ $$$$\:\mathrm{sin}\:{x}=? \\ $$

Question Number 161179 Answers: 0 Comments: 1

Question Number 161178 Answers: 1 Comments: 0

∫^∞ _2 ((arctg(x))/(arctg((x/2))))dx=???

$$\underset{\mathrm{2}} {\int}^{\infty} \frac{\boldsymbol{{arctg}}\left(\boldsymbol{{x}}\right)}{\boldsymbol{{arctg}}\left(\frac{\boldsymbol{{x}}}{\mathrm{2}}\right)}\boldsymbol{{dx}}=??? \\ $$

Question Number 161177 Answers: 1 Comments: 0

Question Number 161176 Answers: 0 Comments: 0

calculate Θ := Σ_(n=1) ^∞ (( (−1 )^( n−1) )/(n ( n + (1/3) ))) =? ■ m.n −−−−−−−−−−−−−

$$ \\ $$$$\:\:\:\:\:\:{calculate}\: \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\:\:\Theta\::=\:\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\:\left(−\mathrm{1}\:\right)^{\:{n}−\mathrm{1}} }{{n}\:\left(\:{n}\:+\:\frac{\mathrm{1}}{\mathrm{3}}\:\right)}\:=?\:\:\:\:\:\:\:\:\:\:\:\:\blacksquare\:\:{m}.{n} \\ $$$$\:\:\:\:\:\:\:−−−−−−−−−−−−− \\ $$$$ \\ $$

Question Number 161169 Answers: 2 Comments: 0

if 9x^2 +(1/x^2 )=3 then 27x^3 +(1/x^3 )=?

$${if}\:\mathrm{9}{x}^{\mathrm{2}} +\frac{\mathrm{1}}{{x}^{\mathrm{2}} }=\mathrm{3} \\ $$$${then} \\ $$$$\:\mathrm{27}{x}^{\mathrm{3}} +\frac{\mathrm{1}}{{x}^{\mathrm{3}} }=? \\ $$

Question Number 161168 Answers: 2 Comments: 1

Show that U_n =((4n−1)/(7n+3)) is convergent sequence.

$${Show}\:{that}\:{U}_{{n}} =\frac{\mathrm{4}{n}−\mathrm{1}}{\mathrm{7}{n}+\mathrm{3}}\:\:{is}\:{convergent}\: \\ $$$${sequence}. \\ $$

Question Number 161166 Answers: 1 Comments: 0

If ^4 log (x+2y) +^4 log (x−2y) = 1 . Minimum value of ∣x∣ − ∣y∣ is ... ?

$${If}\:\:\:^{\mathrm{4}} \mathrm{log}\:\left({x}+\mathrm{2}{y}\right)\:+\:^{\mathrm{4}} \mathrm{log}\:\left({x}−\mathrm{2}{y}\right)\:=\:\mathrm{1}\:. \\ $$$${Minimum}\:\:{value}\:\:{of}\:\:\mid{x}\mid\:−\:\mid{y}\mid\:\:\:{is}\:\:...\:? \\ $$

Question Number 161163 Answers: 1 Comments: 0

Question Number 161162 Answers: 0 Comments: 0

f :]0,+∞[→]0,+∞[ is convex function for n≥2 an integer , prove : (f(1)^(f(1)) f(2)^(f(2)) ...f(n)^(f(n)) )^(1/(f(1)+f(2)+...+f(n))) +(f(1)f(2)...f(n))^(1/n) ≤f(1)+f(n)

$$\left.{f}\::\right]\mathrm{0},+\infty\left[\rightarrow\right]\mathrm{0},+\infty\left[\:{is}\:{convex}\:{function}\right. \\ $$$${for}\:{n}\geqslant\mathrm{2}\:{an}\:{integer}\:,\:{prove}\:: \\ $$$$\left({f}\left(\mathrm{1}\right)^{{f}\left(\mathrm{1}\right)} {f}\left(\mathrm{2}\right)^{{f}\left(\mathrm{2}\right)} ...{f}\left({n}\right)^{{f}\left({n}\right)} \right)^{\frac{\mathrm{1}}{{f}\left(\mathrm{1}\right)+{f}\left(\mathrm{2}\right)+...+{f}\left({n}\right)}} +\left({f}\left(\mathrm{1}\right){f}\left(\mathrm{2}\right)...{f}\left({n}\right)\right)^{\frac{\mathrm{1}}{{n}}} \leqslant{f}\left(\mathrm{1}\right)+{f}\left({n}\right) \\ $$

Question Number 161159 Answers: 2 Comments: 0