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Question Number 207858    Answers: 0   Comments: 1

calculer (1−a)^k /k∈N^

$${calculer}\:\left(\mathrm{1}−{a}\right)^{{k}} \:\:/{k}\in\overset{} {{N}} \\ $$

Question Number 207857    Answers: 1   Comments: 0

∫xtan^(−1) xdx

$$\int{x}\mathrm{tan}^{−\mathrm{1}} {xdx} \\ $$

Question Number 207852    Answers: 2   Comments: 0

Question Number 207846    Answers: 1   Comments: 0

Question Number 207845    Answers: 2   Comments: 0

Find: 1 + (1/(1+2)) + (1/(1+2+3)) +...+ (1/(1+2+3+...+40))

$$\mathrm{Find}: \\ $$$$\mathrm{1}\:+\:\frac{\mathrm{1}}{\mathrm{1}+\mathrm{2}}\:+\:\frac{\mathrm{1}}{\mathrm{1}+\mathrm{2}+\mathrm{3}}\:+...+\:\frac{\mathrm{1}}{\mathrm{1}+\mathrm{2}+\mathrm{3}+...+\mathrm{40}} \\ $$

Question Number 207842    Answers: 1   Comments: 0

(−1)^∞ =?

$$\left(−\mathrm{1}\right)^{\infty} =? \\ $$

Question Number 207834    Answers: 1   Comments: 0

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

Question Number 207833    Answers: 0   Comments: 0

Question Number 207832    Answers: 1   Comments: 1

Prove that Sgn(0)=0

$${Prove}\:{that}\:{Sgn}\left(\mathrm{0}\right)=\mathrm{0} \\ $$

Question Number 207825    Answers: 3   Comments: 0

calculer (1−a)^(k ) :k∈N

$${calculer}\:\left(\mathrm{1}−{a}\right)^{{k}\:\:} \::{k}\in{N} \\ $$

Question Number 207816    Answers: 1   Comments: 1

lim_(x→2) ((((x^2 +4))^(1/3) −(√(x^3 −4)))/( (√(x^2 −4))−((x−2))^(1/3) ))

$$\:\underset{{x}\rightarrow\mathrm{2}} {\mathrm{lim}}\:\frac{\sqrt[{\mathrm{3}}]{\mathrm{x}^{\mathrm{2}} +\mathrm{4}}−\sqrt{\mathrm{x}^{\mathrm{3}} −\mathrm{4}}}{\:\sqrt{\mathrm{x}^{\mathrm{2}} −\mathrm{4}}−\sqrt[{\mathrm{3}}]{\mathrm{x}−\mathrm{2}}} \\ $$

Question Number 207814    Answers: 0   Comments: 1

Some guys are no caught by electricity what′s the reason?

$${Some}\:{guys}\:{are}\:{no}\:{caught}\:{by}\:{electricity} \\ $$$${what}'{s}\:{the}\:{reason}? \\ $$

Question Number 207813    Answers: 1   Comments: 1

the word of atom is meant no dividable however atom is dividable, why we should use the atom word nowadays?

$${the}\:{word}\:{of}\:{atom}\:{is}\:{meant}\:{no}\:{dividable} \\ $$$${however}\:{atom}\:{is}\:{dividable},\:{why}\:{we} \\ $$$${should}\:{use}\:{the}\:{atom}\:{word}\:{nowadays}? \\ $$

Question Number 207812    Answers: 1   Comments: 0

prove that ((vector)/(scalar))=vector

$${prove}\:{that}\:\frac{{vector}}{{scalar}}={vector} \\ $$

Question Number 207810    Answers: 0   Comments: 4

what is the difference between Domain and Codomain?

$${what}\:{is}\:{the}\:{difference}\:{between}\: \\ $$$${Domain}\:{and}\:{Codomain}? \\ $$

Question Number 207805    Answers: 0   Comments: 1

I′ve changed my handset, now unable to view saved equations. How to access saved equatios in new handset?

$$\mathrm{I}'\mathrm{ve}\:\mathrm{changed}\:\mathrm{my}\:\mathrm{handset},\:\mathrm{now}\:\mathrm{unable}\:\mathrm{to}\:\mathrm{view}\:\mathrm{saved}\:\mathrm{equations}. \\ $$$$\mathrm{How}\:\mathrm{to}\:\mathrm{access}\:\mathrm{saved}\:\mathrm{equatios}\:\mathrm{in}\:\mathrm{new}\:\mathrm{handset}? \\ $$

Question Number 207801    Answers: 1   Comments: 1

lim_(t→∞) ∫_0 ^( π) ((sin (tx))/x) dx = ∙∙∙

$$\underset{{t}\rightarrow\infty} {\mathrm{lim}}\:\:\underset{\mathrm{0}} {\overset{\:\:\:\:\:\:\pi} {\int}}\:\:\frac{\mathrm{sin}\:\left(\mathrm{t}{x}\right)}{{x}}\:{dx}\:\:=\:\centerdot\centerdot\centerdot \\ $$

Question Number 207789    Answers: 1   Comments: 0

∀r∈R: H_r =∫_0 ^1 ((t^r −1)/(t−1))dt H_(r+2) −H_r =1 r=?

$$\forall{r}\in\mathbb{R}:\:{H}_{{r}} =\underset{\mathrm{0}} {\overset{\mathrm{1}} {\int}}\:\frac{{t}^{{r}} −\mathrm{1}}{{t}−\mathrm{1}}{dt} \\ $$$${H}_{{r}+\mathrm{2}} −{H}_{{r}} =\mathrm{1} \\ $$$${r}=? \\ $$

Question Number 207787    Answers: 1   Comments: 0

n married couples are invited to a dance party. for the first dance n paires are radomly selected. what′s the probability that no woman dances with her own husband? 1) if a pair must be of different genders. 2) if a pair can also be of the same gender.

$$\boldsymbol{{n}}\:{married}\:{couples}\:{are}\:{invited}\:{to} \\ $$$${a}\:{dance}\:{party}.\:{for}\:{the}\:{first}\:{dance} \\ $$$$\boldsymbol{{n}}\:{paires}\:{are}\:{radomly}\:{selected}.\: \\ $$$${what}'{s}\:{the}\:{probability}\:{that}\:{no}\:{woman} \\ $$$${dances}\:{with}\:{her}\:{own}\:{husband}? \\ $$$$\left.\mathrm{1}\right)\:{if}\:{a}\:{pair}\:{must}\:{be}\:{of}\:{different} \\ $$$$\:\:\:\:\:{genders}. \\ $$$$\left.\mathrm{2}\right)\:{if}\:{a}\:{pair}\:{can}\:{also}\:{be}\:{of}\:{the}\:{same}\: \\ $$$$\:\:\:\:\:{gender}. \\ $$

Question Number 207779    Answers: 1   Comments: 0

Question Number 207774    Answers: 1   Comments: 4

Question Number 207771    Answers: 1   Comments: 0

Simplify: (((b)^(1/4) (√c) − (c)^(1/4) (√b))/( (b)^(1/4) (√c) − (c)^(1/4) )) = ?

$$\mathrm{Simplify}:\:\:\:\:\:\frac{\sqrt[{\mathrm{4}}]{\boldsymbol{\mathrm{b}}}\:\:\sqrt{\boldsymbol{\mathrm{c}}}\:\:−\:\:\sqrt[{\mathrm{4}}]{\boldsymbol{\mathrm{c}}}\:\:\sqrt{\boldsymbol{\mathrm{b}}}}{\:\sqrt[{\mathrm{4}}]{\boldsymbol{\mathrm{b}}}\:\:\sqrt{\boldsymbol{\mathrm{c}}}\:\:−\:\:\sqrt[{\mathrm{4}}]{\boldsymbol{\mathrm{c}}}}\:\:=\:\:? \\ $$

Question Number 207769    Answers: 1   Comments: 1

Question Number 207764    Answers: 3   Comments: 0

Question Number 207753    Answers: 1   Comments: 0

Question Number 207752    Answers: 1   Comments: 3

Two ships have the same berth in a port. It is known that the arrival times of the two ships are independent and have the same probability of docking on a Sunday (00.00−24.00) If the berth time of the first ship is 2 hours and the berth time of the second ship is 4 hours, the probability that one ship will have to wait until the berth can be used is □ ((67)/(144)) □ ((67)/(288)) □ (1/4) □((33)/(144))

$$\:\mathrm{Two}\:\mathrm{ships}\:\mathrm{have}\:\mathrm{the}\:\mathrm{same}\:\mathrm{berth}\: \\ $$$$\:\mathrm{in}\:\mathrm{a}\:\mathrm{port}.\:\mathrm{It}\:\mathrm{is}\:\mathrm{known}\:\mathrm{that}\:\mathrm{the}\: \\ $$$$\:\mathrm{arrival}\:\mathrm{times}\:\mathrm{of}\:\mathrm{the}\:\mathrm{two}\:\mathrm{ships}\: \\ $$$$\:\mathrm{are}\:\mathrm{independent}\:\mathrm{and}\:\mathrm{have}\:\mathrm{the}\: \\ $$$$\:\mathrm{same}\:\mathrm{probability}\:\mathrm{of}\:\mathrm{docking}\: \\ $$$$\mathrm{on}\:\mathrm{a}\:\mathrm{Sunday}\:\left(\mathrm{00}.\mathrm{00}−\mathrm{24}.\mathrm{00}\right) \\ $$$$\:\mathrm{If}\:\mathrm{the}\:\mathrm{berth}\:\mathrm{time}\:\mathrm{of}\:\mathrm{the}\:\mathrm{first}\:\mathrm{ship} \\ $$$$\:\mathrm{is}\:\mathrm{2}\:\mathrm{hours}\:\mathrm{and}\:\mathrm{the}\:\mathrm{berth}\:\mathrm{time} \\ $$$$\:\mathrm{of}\:\mathrm{the}\:\mathrm{second}\:\mathrm{ship}\:\mathrm{is}\:\mathrm{4}\:\mathrm{hours},\: \\ $$$$\:\mathrm{the}\:\mathrm{probability}\:\mathrm{that}\:\mathrm{one}\:\mathrm{ship} \\ $$$$\:\mathrm{will}\:\mathrm{have}\:\mathrm{to}\:\mathrm{wait}\:\mathrm{until}\:\mathrm{the} \\ $$$$\:\mathrm{berth}\:\mathrm{can}\:\mathrm{be}\:\mathrm{used}\:\mathrm{is}\: \\ $$$$\:\Box\:\frac{\mathrm{67}}{\mathrm{144}}\:\:\:\:\:\Box\:\frac{\mathrm{67}}{\mathrm{288}}\:\:\:\:\Box\:\frac{\mathrm{1}}{\mathrm{4}}\:\:\:\:\Box\frac{\mathrm{33}}{\mathrm{144}} \\ $$

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