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Question Number 193982 Answers: 3 Comments: 0

∫ ((6x^3 +9x^2 +15x+6)/( (√(x^2 +x+1)))) dx =?

$$\:\:\:\:\:\int\:\frac{\mathrm{6x}^{\mathrm{3}} +\mathrm{9x}^{\mathrm{2}} +\mathrm{15x}+\mathrm{6}}{\:\sqrt{\mathrm{x}^{\mathrm{2}} +\mathrm{x}+\mathrm{1}}}\:\mathrm{dx}\:=? \\ $$

Question Number 193981 Answers: 0 Comments: 0

Question Number 193978 Answers: 1 Comments: 0

Question Number 193976 Answers: 2 Comments: 0

Question Number 193975 Answers: 2 Comments: 1

Question Number 193972 Answers: 0 Comments: 4

Question Number 193971 Answers: 2 Comments: 0

y= ⌊ x^( 2) ⌋ + ⌊ x ⌋ ⇒ R_y =? Range

$$ \\ $$$$\:\:\:\:\:\:{y}=\:\lfloor\:{x}^{\:\mathrm{2}} \:\rfloor\:+\:\lfloor\:{x}\:\rfloor\:\: \\ $$$$\:\: \\ $$$$\:\:\:\:\:\:\:\Rightarrow\:\:{R}_{{y}} \:=?\:\:\:\:\:\:\:{Range} \\ $$

Question Number 193965 Answers: 2 Comments: 0

a,b,c are positive real numbers And (1/(a+b+1))+(1/(b+c+1))+(1/(a+c+1))≥1 prove that a+b+c≥ab+bc+ac

$${a},{b},{c}\:{are}\:{positive}\:{real}\:{numbers} \\ $$$${And} \\ $$$$\frac{\mathrm{1}}{{a}+{b}+\mathrm{1}}+\frac{\mathrm{1}}{{b}+{c}+\mathrm{1}}+\frac{\mathrm{1}}{{a}+{c}+\mathrm{1}}\geqslant\mathrm{1} \\ $$$${prove}\:{that}\:{a}+{b}+{c}\geqslant{ab}+{bc}+{ac} \\ $$

Question Number 193962 Answers: 2 Comments: 0

Question Number 194691 Answers: 0 Comments: 0

a, b, c≥0, a+b+c=2. Prove that 3a+8ab+16abc≤12.

$${a},\:{b},\:{c}\geqslant\mathrm{0},\:{a}+{b}+{c}=\mathrm{2}.\:\mathrm{Prove}\:\mathrm{that} \\ $$$$\mathrm{3}{a}+\mathrm{8}{ab}+\mathrm{16}{abc}\leqslant\mathrm{12}. \\ $$

Question Number 194689 Answers: 1 Comments: 0

Question Number 194688 Answers: 1 Comments: 0

find all function f: R → R such that ∀x, y∈R, f(x−f(y))=f(f(y))+xf(y)+f(x)−1.

$$\mathrm{find}\:\mathrm{all}\:\mathrm{function}\:{f}:\:\mathbb{R}\:\rightarrow\:\mathbb{R}\:\mathrm{such}\:\mathrm{that}\:\forall{x},\:{y}\in\mathbb{R}, \\ $$$${f}\left({x}−{f}\left({y}\right)\right)={f}\left({f}\left({y}\right)\right)+{xf}\left({y}\right)+{f}\left({x}\right)−\mathrm{1}. \\ $$

Question Number 193958 Answers: 1 Comments: 0

Question Number 193951 Answers: 2 Comments: 0

Prove that: lim_(n→+∞) (1/(n!))∫^( n) _( 0) t^n e^(−t) dt = (1/2)

$$\mathrm{Prove}\:\mathrm{that}: \\ $$$$\underset{\mathrm{n}\rightarrow+\infty} {\mathrm{lim}}\:\frac{\mathrm{1}}{\mathrm{n}!}\underset{\:\mathrm{0}} {\int}^{\:\mathrm{n}} {t}^{{n}} {e}^{−{t}} {dt}\:=\:\frac{\mathrm{1}}{\mathrm{2}} \\ $$

Question Number 193953 Answers: 3 Comments: 0

Name thefollowing Complex compound (a)[Zn(en)_2 (c_2 o_2 )Br_2 F]^(−5) (b)Ni(CN)_2 (OH)_3 Cl] [Fe(H_2 O)_3 (OH)_2 F_2 Br] (c)[Cr(CN)_4 NO_2 (H_2 O)_2 (NH_3 )_2 ]^(2−)

$${Name}\:{thefollowing}\:{Complex}\:{compound} \\ $$$$\left({a}\right)\left[{Zn}\left({en}\right)_{\mathrm{2}} \left({c}_{\mathrm{2}} {o}_{\mathrm{2}} \right){Br}_{\mathrm{2}} {F}\right]^{−\mathrm{5}} \\ $$$$\left.\left({b}\right){Ni}\left({CN}\right)_{\mathrm{2}} \left({OH}\right)_{\mathrm{3}} {Cl}\right]\:\:\left[{Fe}\left({H}_{\mathrm{2}} {O}\right)_{\mathrm{3}} \left({OH}\right)_{\mathrm{2}} {F}_{\mathrm{2}} {Br}\right] \\ $$$$\left({c}\right)\left[{Cr}\left({CN}\right)_{\mathrm{4}} {NO}_{\mathrm{2}} \left({H}_{\mathrm{2}} {O}\right)_{\mathrm{2}} \left({NH}_{\mathrm{3}} \right)_{\mathrm{2}} \:\right]^{\mathrm{2}−} \\ $$

Question Number 193949 Answers: 3 Comments: 0

Question Number 193938 Answers: 4 Comments: 0

Question Number 193924 Answers: 1 Comments: 2

question about tinkutara how can an answer be placed in a box.

$$\:\:\underline{\mathrm{question}\:\mathrm{about}\:\mathrm{tinkutara}} \\ $$$$\:\:\mathrm{how}\:\mathrm{can}\:\mathrm{an}\:\mathrm{answer}\:\mathrm{be}\:\mathrm{placed}\:\: \\ $$$$\:\:\mathrm{in}\:\mathrm{a}\:\mathrm{box}. \\ $$

Question Number 193922 Answers: 4 Comments: 0

Question Number 193921 Answers: 0 Comments: 0

Show that the kernel of a group homomorhism θ : G → H is a normal subgroup. Hint: Check the existence of the combination g^(−1) kg in the kernel.

$$\mathrm{Show}\:\mathrm{that}\:\mathrm{the}\:\mathrm{kernel}\:\mathrm{of}\:\mathrm{a}\:\mathrm{group}\:\mathrm{homomorhism} \\ $$$$\theta\::\:\mathrm{G}\:\rightarrow\:\mathrm{H}\:\mathrm{is}\:\mathrm{a}\:\mathrm{normal}\:\mathrm{subgroup}. \\ $$$$\mathrm{Hint}:\:\mathrm{Check}\:\mathrm{the}\:\mathrm{existence}\:\mathrm{of}\:\mathrm{the}\:\mathrm{combination} \\ $$$$\mathrm{g}^{−\mathrm{1}} \mathrm{kg}\:\mathrm{in}\:\mathrm{the}\:\mathrm{kernel}. \\ $$

Question Number 193918 Answers: 0 Comments: 0

Question Number 193908 Answers: 2 Comments: 0

Question Number 193906 Answers: 1 Comments: 0

Question Number 193896 Answers: 0 Comments: 0

Ques. 12 If Y = {0, 1, 2, 3, 4} is transversal for 5Z in (Z, +). Show whether or not Y is a subgroup of 5Z subgroup under addition of integers modulo of 5

$$\mathrm{Ques}.\:\mathrm{12} \\ $$$$\mathrm{If}\:\mathrm{Y}\:=\:\left\{\mathrm{0},\:\mathrm{1},\:\mathrm{2},\:\mathrm{3},\:\mathrm{4}\right\}\:\mathrm{is}\:\mathrm{transversal}\:\mathrm{for}\:\mathrm{5}\mathbb{Z} \\ $$$$\mathrm{in}\:\left(\mathbb{Z},\:+\right).\:\mathrm{Show}\:\mathrm{whether}\:\mathrm{or}\:\mathrm{not}\:\mathrm{Y}\:\mathrm{is}\:\mathrm{a}\: \\ $$$$\mathrm{subgroup}\:\mathrm{of}\:\mathrm{5}\mathbb{Z}\: \\ $$$$ \\ $$$$\mathrm{subgroup}\:\mathrm{under}\:\mathrm{addition}\:\mathrm{of}\:\mathrm{integers}\:\mathrm{modulo} \\ $$$$\mathrm{of}\:\mathrm{5} \\ $$

Question Number 193893 Answers: 1 Comments: 0

Ques. 11 Let {H_α } ∈ Ω be a family of subgroup of a group G then prove that ∩_(α=Ω) H_α is also a subgroup Ques. 12 Using GAP, find the elements A, B and C in D_5 such that AB = BC but A ≠ C.

$$\mathrm{Ques}.\:\mathrm{11} \\ $$$$\:\:\:\:\:\mathrm{Let}\:\left\{\mathrm{H}_{\alpha} \right\}\:\in\:\Omega\:\mathrm{be}\:\mathrm{a}\:\mathrm{family}\:\mathrm{of}\:\mathrm{subgroup}\:\mathrm{of} \\ $$$$\mathrm{a}\:\mathrm{group}\:\mathrm{G}\:\mathrm{then}\:\mathrm{prove}\:\mathrm{that}\:\underset{\alpha=\Omega} {\cap}\mathrm{H}_{\alpha} \:\mathrm{is}\:\mathrm{also}\:\mathrm{a} \\ $$$$\mathrm{subgroup} \\ $$$$ \\ $$$$\mathrm{Ques}.\:\mathrm{12}\: \\ $$$$\:\:\:\:\:\mathrm{Using}\:\mathrm{GAP},\:\mathrm{find}\:\mathrm{the}\:\mathrm{elements}\:\mathrm{A},\:\mathrm{B}\:\mathrm{and}\: \\ $$$$\mathrm{C}\:\mathrm{in}\:\mathrm{D}_{\mathrm{5}} \:\mathrm{such}\:\mathrm{that}\:\mathrm{AB}\:=\:\mathrm{BC}\:\mathrm{but}\:\mathrm{A}\:\neq\:\mathrm{C}. \\ $$

Question Number 193892 Answers: 2 Comments: 0

Ques. Find the number of integers in the set S={1,2,3,...,60} which are not divisible by 2 nor by 3 nor by 5. Hello

$$\mathrm{Ques}. \\ $$$$\:\:\:\:\:\mathrm{Find}\:\mathrm{the}\:\mathrm{number}\:\mathrm{of}\:\mathrm{integers}\:\mathrm{in}\:\mathrm{the}\:\mathrm{set} \\ $$$$\mathrm{S}=\left\{\mathrm{1},\mathrm{2},\mathrm{3},...,\mathrm{60}\right\}\:\mathrm{which}\:\mathrm{are}\:\mathrm{not}\:\mathrm{divisible} \\ $$$$\mathrm{by}\:\mathrm{2}\:\mathrm{nor}\:\mathrm{by}\:\mathrm{3}\:\mathrm{nor}\:\mathrm{by}\:\mathrm{5}. \\ $$$$ \\ $$$$\mathrm{Hello} \\ $$

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