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AllQuestion and Answers: Page 62

Question Number 218311 Answers: 1 Comments: 0

Question Number 218267 Answers: 1 Comments: 1

Question Number 218265 Answers: 1 Comments: 0

can interpret the metric Tensor g_(μν) is kinda distance function at curved Surface ?? ex. Euclidean space g_(μν) = ((1,0,0),(0,1,0),(0,0,1) ) Sphere g_(μν) = ((( 1),( 0),( 0)),(( 0),( r^2 ),( 0)),(( 0),( 0),(r^2 sin^2 (θ))) )

$$\mathrm{can}\:\mathrm{interpret}\:\mathrm{the}\:\mathrm{metric}\:\mathrm{Tensor}\:\boldsymbol{\mathrm{g}}_{\mu\nu} \:\mathrm{is}\: \\ $$$$\mathrm{kinda}\:\mathrm{distance}\:\mathrm{function}\:\mathrm{at}\:\mathrm{curved}\:\mathrm{Surface}\:?? \\ $$$$\mathrm{ex}.\:\mathrm{Euclidean}\:\mathrm{space}\:\boldsymbol{\mathrm{g}}_{\mu\nu} =\begin{pmatrix}{\mathrm{1}}&{\mathrm{0}}&{\mathrm{0}}\\{\mathrm{0}}&{\mathrm{1}}&{\mathrm{0}}\\{\mathrm{0}}&{\mathrm{0}}&{\mathrm{1}}\end{pmatrix} \\ $$$$\mathrm{Sphere}\:\boldsymbol{\mathrm{g}}_{\mu\nu} =\begin{pmatrix}{\:\mathrm{1}}&{\:\:\:\:\mathrm{0}}&{\:\:\:\:\:\:\:\mathrm{0}}\\{\:\mathrm{0}}&{\:\:\:\:{r}^{\mathrm{2}} }&{\:\:\:\:\:\:\:\mathrm{0}}\\{\:\mathrm{0}}&{\:\:\:\:\:\mathrm{0}}&{{r}^{\mathrm{2}} \mathrm{sin}^{\mathrm{2}} \left(\theta\right)}\end{pmatrix} \\ $$

Question Number 218262 Answers: 1 Comments: 1

Question Number 218257 Answers: 1 Comments: 2

Question Number 218256 Answers: 2 Comments: 0

Question Number 218255 Answers: 0 Comments: 0

Question Number 218236 Answers: 1 Comments: 3

Question Number 218221 Answers: 1 Comments: 7

Question Number 218208 Answers: 1 Comments: 1

This question is really important Prove or disprove that lim_(n→∞) ((3^n m+3^(n−1) )/2^(⌈(n/2)⌉) ) + (3^(n−1) /2^n ) the limit exists for m ∈ N \B where B = {n ∣ log_2 (n) ∈ N }

$${This}\:{question}\:{is}\:{really}\:{important} \\ $$$${Prove}\:{or}\:{disprove}\:{that} \\ $$$$\underset{{n}\rightarrow\infty} {\mathrm{lim}}\:\frac{\mathrm{3}^{{n}} {m}+\mathrm{3}^{{n}−\mathrm{1}} }{\mathrm{2}^{\lceil\frac{{n}}{\mathrm{2}}\rceil} }\:+\:\frac{\mathrm{3}^{{n}−\mathrm{1}} }{\mathrm{2}^{{n}} }\: \\ $$$$\:{the}\:{limit}\:{exists}\:{for}\:{m}\:\in\:{N}\:\backslash{B} \\ $$$${where}\:{B}\:=\:\left\{{n}\:\mid\:{log}_{\mathrm{2}} \left({n}\right)\:\in\:{N}\:\right\} \\ $$

Question Number 218206 Answers: 0 Comments: 0

Question Number 218202 Answers: 0 Comments: 3

Question Number 218199 Answers: 1 Comments: 0

describes the rupture body onQ of polynomials. a) X^5 +1 b) X^6 −X^3 +1

$${describes}\:{the}\:{rupture}\:{body}\:{onQ} \\ $$$${of}\:{polynomials}. \\ $$$$\left.{a}\left.\right)\:{X}^{\mathrm{5}} +\mathrm{1}\:\:\:\:\:\:\:\:\:{b}\right)\:{X}^{\mathrm{6}} −{X}^{\mathrm{3}} +\mathrm{1} \\ $$

Question Number 218191 Answers: 0 Comments: 0

exercises algebra. all algebraically closed fields ares finite. prouve it .

$${exercises}\:{algebra}. \\ $$$${all}\:\:{algebraically}\:\:{closed}\:\:{fields} \\ $$$${ares}\:{finite}. \\ $$$${prouve}\:\:{it}\:. \\ $$

Question Number 218189 Answers: 0 Comments: 0

Question Number 218188 Answers: 0 Comments: 0

Question Number 218187 Answers: 1 Comments: 0

Question Number 218185 Answers: 1 Comments: 0

Find: lim_(n→∞) sin (nπ (√(n^2 + 2n + 2∙(k + 1)))) = ? k ∈ Z - fixed

$$\mathrm{Find}: \\ $$$$\underset{\boldsymbol{\mathrm{n}}\rightarrow\infty} {\mathrm{lim}}\:\mathrm{sin}\:\left(\mathrm{n}\pi\:\sqrt{\mathrm{n}^{\mathrm{2}} \:+\:\mathrm{2n}\:+\:\mathrm{2}\centerdot\left(\mathrm{k}\:+\:\mathrm{1}\right)}\right)\:=\:? \\ $$$$\mathrm{k}\:\in\:\mathbb{Z}\:-\:\mathrm{fixed} \\ $$

Question Number 218184 Answers: 1 Comments: 0

− 2025 : 7 Residue = ?

$$−\:\mathrm{2025}\:\::\:\:\mathrm{7} \\ $$$$\mathrm{Residue}\:=\:? \\ $$

Question Number 218196 Answers: 3 Comments: 0

lim _(n→∞) (1/n) ( (((2n)!)/(n!)) )^(1/n) = ?

$$ \\ $$$$ \\ $$$$\:\:\:\:\mathrm{lim}\:_{\mathrm{n}\rightarrow\infty} \frac{\mathrm{1}}{{n}}\:\left(\:\frac{\left(\mathrm{2}{n}\right)!}{{n}!}\:\right)^{\frac{\mathrm{1}}{{n}}} =\:?\:\:\:\:\:\:\:\: \\ $$$$ \\ $$

Question Number 218195 Answers: 1 Comments: 0

P=((ΣFz)/(Npil))

$${P}=\frac{\Sigma{Fz}}{{Npil}} \\ $$

Question Number 218183 Answers: 1 Comments: 0

Find: (√(33^2 + 544^2 )) + (√(333^2 + 55444^2 )) = ?

$$\mathrm{Find}: \\ $$$$\sqrt{\mathrm{33}^{\mathrm{2}} \:\:+\:\:\mathrm{544}^{\mathrm{2}} }\:\:+\:\:\sqrt{\mathrm{333}^{\mathrm{2}} \:\:+\:\:\mathrm{55444}^{\mathrm{2}} }\:\:=\:\:? \\ $$

Question Number 218169 Answers: 0 Comments: 0

P(5,6)=((15!)/((15−6))) = ((15!)/(9!)) =((15×14×131×2×11×10×9×8×7×6×5×4×3×2×1)/(9×8×7×6×5×4×3×2×)) =15×14×13×12×11×10 =3,603,600

$${P}\left(\mathrm{5},\mathrm{6}\right)=\frac{\mathrm{15}!}{\left(\mathrm{15}−\mathrm{6}\right)}\:=\:\frac{\mathrm{15}!}{\mathrm{9}!}\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:=\frac{\mathrm{15}×\mathrm{14}×\mathrm{131}×\mathrm{2}×\mathrm{11}×\mathrm{10}×\mathrm{9}×\mathrm{8}×\mathrm{7}×\mathrm{6}×\mathrm{5}×\mathrm{4}×\mathrm{3}×\mathrm{2}×\mathrm{1}}{\mathrm{9}×\mathrm{8}×\mathrm{7}×\mathrm{6}×\mathrm{5}×\mathrm{4}×\mathrm{3}×\mathrm{2}×} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:=\mathrm{15}×\mathrm{14}×\mathrm{13}×\mathrm{12}×\mathrm{11}×\mathrm{10} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:=\mathrm{3},\mathrm{603},\mathrm{600} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\: \\ $$

Question Number 218165 Answers: 2 Comments: 0

λ > 0 x , y , z ∈ C Solve the system: { ((xy = z^2 + 2λz − λx − λy)),((yz = x^2 + 2λx − λy − λz )),((zx = y^2 + 2λy − λz − λx)) :}

$$\lambda\:>\:\mathrm{0} \\ $$$$\mathrm{x}\:,\:\mathrm{y}\:,\:\mathrm{z}\:\in\:\mathrm{C} \\ $$$$\mathrm{Solve}\:\mathrm{the}\:\mathrm{system}:\:\:\:\begin{cases}{\mathrm{xy}\:=\:\mathrm{z}^{\mathrm{2}} \:+\:\mathrm{2}\lambda\mathrm{z}\:−\:\lambda\mathrm{x}\:−\:\lambda\mathrm{y}}\\{\mathrm{yz}\:=\:\mathrm{x}^{\mathrm{2}} \:+\:\mathrm{2}\lambda\mathrm{x}\:−\:\lambda\mathrm{y}\:−\:\lambda\mathrm{z}\:\:\:\:\:\:\:\:}\\{\mathrm{zx}\:=\:\mathrm{y}^{\mathrm{2}} \:+\:\mathrm{2}\lambda\mathrm{y}\:−\:\lambda\mathrm{z}\:−\:\lambda\mathrm{x}}\end{cases} \\ $$

Question Number 218153 Answers: 3 Comments: 0

x+y =12 minimum value of (√(x^2 +4)) +(√(y^2 +9)) =?

$$\:{x}+{y}\:=\mathrm{12} \\ $$$$\:{minimum}\:{value}\:{of} \\ $$$$\:\sqrt{{x}^{\mathrm{2}} +\mathrm{4}}\:+\sqrt{{y}^{\mathrm{2}} +\mathrm{9}}\:=? \\ $$

Question Number 218150 Answers: 1 Comments: 0

∫_0 ^1 (1/(1−x^2 ))ln(((1+x)/(2x)))dx

$$\int_{\mathrm{0}} ^{\mathrm{1}} \frac{\mathrm{1}}{\mathrm{1}−{x}^{\mathrm{2}} }{ln}\left(\frac{\mathrm{1}+{x}}{\mathrm{2}{x}}\right){dx} \\ $$

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