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Question Number 148558 Answers: 2 Comments: 0

Trouver toutes les fonctions continues f:R→R verifiant: ∀(x,y)∈R^2 , f(x+y)f(x−y)=f^2 (x)f^2 (y).. monsieur j′ai suppose^ que f est un morphisme mutiplicatif de R.. mais ca ne sort pas...

$$\mathrm{Trouver}\:\mathrm{toutes}\:\mathrm{les}\:\mathrm{fonctions}\:\mathrm{continues} \\ $$$$\mathrm{f}:\mathbb{R}\rightarrow\mathbb{R}\:\mathrm{verifiant}: \\ $$$$\forall\left(\mathrm{x},\mathrm{y}\right)\in\mathbb{R}^{\mathrm{2}} ,\:\mathrm{f}\left(\mathrm{x}+\mathrm{y}\right)\mathrm{f}\left(\mathrm{x}−\mathrm{y}\right)=\mathrm{f}^{\mathrm{2}} \left(\mathrm{x}\right)\mathrm{f}^{\mathrm{2}} \left(\mathrm{y}\right).. \\ $$$$\mathrm{monsieur}\:\mathrm{j}'\mathrm{ai}\:\mathrm{suppos}\acute {\mathrm{e}}\:\mathrm{que}\:\mathrm{f}\:\mathrm{est}\:\mathrm{un}\: \\ $$$$\mathrm{morphisme}\:\mathrm{mutiplicatif}\:\mathrm{de}\:\mathbb{R}..\:\mathrm{mais}\:\mathrm{ca}\:\mathrm{ne} \\ $$$$\mathrm{sort}\:\mathrm{pas}... \\ $$

Question Number 148550 Answers: 1 Comments: 2

A(0;0) ; B(−2;4) and C(−6;14) if the triangle has vertices, find the lenght of the median drawn from the vertx C

$$\boldsymbol{{A}}\left(\mathrm{0};\mathrm{0}\right)\:\:;\:\:\boldsymbol{{B}}\left(−\mathrm{2};\mathrm{4}\right)\:\:{and}\:\:\boldsymbol{{C}}\left(−\mathrm{6};\mathrm{14}\right) \\ $$$${if}\:{the}\:{triangle}\:{has}\:{vertices},\:{find}\:{the} \\ $$$${lenght}\:{of}\:{the}\:{median}\:{drawn}\:{from} \\ $$$${the}\:{vertx}\:\boldsymbol{{C}} \\ $$

Question Number 148552 Answers: 0 Comments: 2

Question Number 148546 Answers: 3 Comments: 2

lim_(x→0) (((√(x + 4)) - 2)/(sinx)) = ?

$$\underset{\boldsymbol{{x}}\rightarrow\mathrm{0}} {{lim}}\:\frac{\sqrt{{x}\:+\:\mathrm{4}}\:-\:\mathrm{2}}{{sinx}}\:=\:? \\ $$

Question Number 148543 Answers: 4 Comments: 0

Question Number 148541 Answers: 1 Comments: 0

Question Number 148540 Answers: 1 Comments: 0

Question Number 148534 Answers: 1 Comments: 8

Question Number 148525 Answers: 2 Comments: 0

Express (((√(15))+(√(35))+(√(21))+5)/( (√3)+2(√5)+(√7))) in the form a(√(3 ))+ b(√7).

$$\:\mathrm{Express}\:\:\frac{\sqrt{\mathrm{15}}+\sqrt{\mathrm{35}}+\sqrt{\mathrm{21}}+\mathrm{5}}{\:\sqrt{\mathrm{3}}+\mathrm{2}\sqrt{\mathrm{5}}+\sqrt{\mathrm{7}}}\:\mathrm{in}\:\mathrm{the}\:\mathrm{form} \\ $$$$\:{a}\sqrt{\mathrm{3}\:}+\:{b}\sqrt{\mathrm{7}}. \\ $$

Question Number 148522 Answers: 2 Comments: 0

Question Number 148519 Answers: 0 Comments: 1

a_n =(n/(n+1)) let ε>0 be given, ∣a_m −a_n ∣=∣(m/(m+1))−(n/(n+1))∣=∣((m−n)/((m+1)(n+1)))∣=((m−n)/((m+1)(n+1))) provided m>n, ((m−n)/((m+1)(n+1)))<((m+1)/((m+1)(n+1)))=(1/(n+1))<ε. if N>((1−ε)/ε) then ∣a_m −a_n ∣<ε ∀ n,m≥N

$$ \\ $$$$\mathrm{a}_{\mathrm{n}} =\frac{\mathrm{n}}{\mathrm{n}+\mathrm{1}} \\ $$$$\mathrm{let}\:\epsilon>\mathrm{0}\:\mathrm{be}\:\mathrm{given},\:\mid\mathrm{a}_{\mathrm{m}} −\mathrm{a}_{\mathrm{n}} \mid=\mid\frac{\mathrm{m}}{\mathrm{m}+\mathrm{1}}−\frac{\mathrm{n}}{\mathrm{n}+\mathrm{1}}\mid=\mid\frac{\mathrm{m}−\mathrm{n}}{\left(\mathrm{m}+\mathrm{1}\right)\left(\mathrm{n}+\mathrm{1}\right)}\mid=\frac{\mathrm{m}−\mathrm{n}}{\left(\mathrm{m}+\mathrm{1}\right)\left(\mathrm{n}+\mathrm{1}\right)}\:\mathrm{provided} \\ $$$$\mathrm{m}>\mathrm{n},\:\frac{\mathrm{m}−\mathrm{n}}{\left(\mathrm{m}+\mathrm{1}\right)\left(\mathrm{n}+\mathrm{1}\right)}<\frac{\mathrm{m}+\mathrm{1}}{\left(\mathrm{m}+\mathrm{1}\right)\left(\mathrm{n}+\mathrm{1}\right)}=\frac{\mathrm{1}}{\mathrm{n}+\mathrm{1}}<\epsilon.\:\mathrm{if}\:\mathrm{N}>\frac{\mathrm{1}−\epsilon}{\epsilon}\:\mathrm{then}\:\mid\mathrm{a}_{\mathrm{m}} −\mathrm{a}_{\mathrm{n}} \mid<\epsilon\:\forall\:\mathrm{n},\mathrm{m}\geqslant\mathrm{N} \\ $$

Question Number 148515 Answers: 1 Comments: 0

Find the sum of the roots of the equation: x^2 - 2x - 3 ∣x - 1∣ + 3 = 0

$${Find}\:{the}\:{sum}\:{of}\:{the}\:{roots}\:{of}\:{the}\:{equation}: \\ $$$${x}^{\mathrm{2}} \:-\:\mathrm{2}{x}\:-\:\mathrm{3}\:\mid{x}\:-\:\mathrm{1}\mid\:+\:\mathrm{3}\:=\:\mathrm{0} \\ $$

Question Number 148532 Answers: 1 Comments: 0