Question and Answers Forum

AllQuestion and Answers: Page 1

Question Number 228534 Answers: 0 Comments: 0

analysis show that lim_(n→∞) (1+(z/n))^n =e^z . uniformly convergence for all 𝛜>0 there exist N∈N whenever z∈E such that N<n ⇒ ∣f_n (z)−f(z)∣<𝛜

$$\mathrm{analysis} \\ $$$$\mathrm{show}\:\mathrm{that}\:\underset{{n}\rightarrow\infty} {\mathrm{lim}}\left(\mathrm{1}+\frac{{z}}{{n}}\right)^{{n}} ={e}^{{z}} . \\ $$$$\boldsymbol{\mathrm{uniformly}}\:\boldsymbol{\mathrm{convergence}} \\ $$$$\boldsymbol{\mathrm{for}}\:\boldsymbol{\mathrm{all}}\:\boldsymbol{\varepsilon}>\mathrm{0}\:\boldsymbol{\mathrm{there}}\:\boldsymbol{\mathrm{exist}}\:\boldsymbol{{N}}\in\mathbb{N}\:\boldsymbol{\mathrm{whenever}}\:{z}\in\mathbb{E} \\ $$$$\boldsymbol{\mathrm{such}}\:\boldsymbol{\mathrm{that}}\:\boldsymbol{{N}}<\boldsymbol{{n}}\:\Rightarrow\:\mid{f}_{{n}} \left({z}\right)−{f}\left({z}\right)\mid<\boldsymbol{\varepsilon} \\ $$

Question Number 228528 Answers: 0 Comments: 0

Question Number 228525 Answers: 0 Comments: 0

pn(x) = log_π (x) ln(x) = ln(π) × pn(x) my new fonction

$${pn}\left({x}\right)\:=\:{log}_{\pi} \left({x}\right) \\ $$$${ln}\left({x}\right)\:=\:{ln}\left(\pi\right)\:×\:{pn}\left({x}\right) \\ $$$${my}\:{new}\:{fonction} \\ $$

Question Number 228523 Answers: 0 Comments: 7

inversion of question 228499 find one cubic y=ax^3 +bx^2 +cx+d with 3 real zeros which touches these 3 parabolas: y=−5x^2 y=−(1/7)x^2 y=(2/3)x^2 (it′s possible!)

$$\mathrm{inversion}\:\mathrm{of}\:\mathrm{question}\:\mathrm{228499} \\ $$$$ \\ $$$$\mathrm{find}\:\mathrm{one}\:\mathrm{cubic} \\ $$$${y}={ax}^{\mathrm{3}} +{bx}^{\mathrm{2}} +{cx}+{d} \\ $$$$\mathrm{with}\:\mathrm{3}\:\mathrm{real}\:\mathrm{zeros}\:\mathrm{which}\:\mathrm{touches}\:\mathrm{these} \\ $$$$\mathrm{3}\:\mathrm{parabolas}: \\ $$$${y}=−\mathrm{5}{x}^{\mathrm{2}} \\ $$$${y}=−\frac{\mathrm{1}}{\mathrm{7}}{x}^{\mathrm{2}} \\ $$$${y}=\frac{\mathrm{2}}{\mathrm{3}}{x}^{\mathrm{2}} \\ $$$$ \\ $$$$\left(\mathrm{it}'\mathrm{s}\:\mathrm{possible}!\right) \\ $$

Question Number 228520 Answers: 0 Comments: 0

Question Number 228511 Answers: 0 Comments: 2

Question Number 228499 Answers: 3 Comments: 1

Question Number 228478 Answers: 0 Comments: 4

a,b,c,d ∈ R a(1−a) + b(3−b) + c(5−c) + d(7−d) Find: max(a,b,c,d) = ?

$$\mathrm{a},\mathrm{b},\mathrm{c},\mathrm{d}\:\in\:\mathbb{R} \\ $$$$\mathrm{a}\left(\mathrm{1}−\mathrm{a}\right)\:+\:\mathrm{b}\left(\mathrm{3}−\mathrm{b}\right)\:+\:\mathrm{c}\left(\mathrm{5}−\mathrm{c}\right)\:+\:\mathrm{d}\left(\mathrm{7}−\mathrm{d}\right) \\ $$$$\mathrm{Find}:\:\:\:\boldsymbol{\mathrm{max}}\left(\mathrm{a},\mathrm{b},\mathrm{c},\mathrm{d}\right)\:=\:? \\ $$

Question Number 228474 Answers: 3 Comments: 2

Question Number 228464 Answers: 1 Comments: 1

∫xsin^(−1) xdx

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

Question Number 228455 Answers: 3 Comments: 2

Question Number 228451 Answers: 1 Comments: 0

Question Number 228448 Answers: 1 Comments: 0

Question Number 228440 Answers: 1 Comments: 0

3^x +9^x +27^x =14

$$\mathrm{3}^{{x}} +\mathrm{9}^{{x}} +\mathrm{27}^{{x}} =\mathrm{14} \\ $$

Question Number 228431 Answers: 1 Comments: 0

(a)1324 (b) 1326 (c) 1328 (d) 1330 (d) 1332

$$\:\: \\ $$$$ \\ $$$$ \\ $$$$ \\ $$$$ \left({a}\right)\mathrm{1324}\:\:\:\:\left({b}\right)\:\mathrm{1326}\:\:\:\:\:\left({c}\right)\:\mathrm{1328}\:\:\:\:\:\left({d}\right)\:\mathrm{1330}\:\:\:\:\left({d}\right)\:\mathrm{1332}\: \\ $$

Question Number 228430 Answers: 1 Comments: 0

Question Number 228414 Answers: 2 Comments: 3

Question Number 228417 Answers: 1 Comments: 4

Question Number 228378 Answers: 2 Comments: 1

Question Number 228366 Answers: 0 Comments: 0

calculer la limite suivante lim_(x→0) ((1/k))!×Π_(k=0) ^(n−1) cos (((E(kx))/(k!)))

$$\mathrm{calculer}\:\mathrm{la}\:\mathrm{limite}\:\mathrm{suivante}\: \\ $$$$\:\:\:\:\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\left(\frac{\mathrm{1}}{\mathrm{k}}\right)!×\underset{\mathrm{k}=\mathrm{0}} {\overset{\mathrm{n}−\mathrm{1}} {\prod}}\mathrm{cos}\:\left(\frac{\mathrm{E}\left(\mathrm{kx}\right)}{\mathrm{k}!}\right) \\ $$

Question Number 228358 Answers: 3 Comments: 0

Find: lim_(x→(𝛑/2)) [(x − (π/2)) tanx] = ?

$$\mathrm{Find}:\:\:\:\underset{\boldsymbol{\mathrm{x}}\rightarrow\frac{\boldsymbol{\pi}}{\mathrm{2}}} {\mathrm{lim}}\:\left[\left(\mathrm{x}\:−\:\frac{\pi}{\mathrm{2}}\right)\:\mathrm{tanx}\right]\:=\:? \\ $$

Question Number 228347 Answers: 0 Comments: 0

Question Number 228342 Answers: 2 Comments: 9

Question Number 228339 Answers: 2 Comments: 0

Question Number 228335 Answers: 1 Comments: 0

x+(1/x)=(√3) x^(30) +x^(24) +x^(18) +x^(12) +x^6 +1=?

$${x}+\frac{\mathrm{1}}{{x}}=\sqrt{\mathrm{3}} \\ $$$${x}^{\mathrm{30}} +{x}^{\mathrm{24}} +{x}^{\mathrm{18}} +{x}^{\mathrm{12}} +{x}^{\mathrm{6}} +\mathrm{1}=? \\ $$

Question Number 228331 Answers: 1 Comments: 0

x=(((√2)+1)/( (√2)−1)) &x−y=4(√2) x^4 +y^4 =?

$${x}=\frac{\sqrt{\mathrm{2}}+\mathrm{1}}{\:\sqrt{\mathrm{2}}−\mathrm{1}}\:\&{x}−{y}=\mathrm{4}\sqrt{\mathrm{2}} \\ $$$${x}^{\mathrm{4}} +{y}^{\mathrm{4}} =? \\ $$

Pg 1 Pg 2 Pg 3 Pg 4 Pg 5 Pg 6 Pg 7 Pg 8 Pg 9 Pg 10

Contact: [email protected]