Question and Answers Forum

AlgebraQuestion and Answers: Page 86

Question Number 186053 Answers: 2 Comments: 0

Question Number 186025 Answers: 0 Comments: 1

P(x) = −3x^2 +5x^3 +5x^2 −5x−2 division euclidienne par x^2 −1

$$\boldsymbol{\mathrm{P}}\left(\boldsymbol{{x}}\right)\:=\:−\mathrm{3}\boldsymbol{\mathrm{x}}^{\mathrm{2}} +\mathrm{5}\boldsymbol{\mathrm{x}}^{\mathrm{3}} +\mathrm{5}\boldsymbol{\mathrm{x}}^{\mathrm{2}} −\mathrm{5}\boldsymbol{\mathrm{x}}−\mathrm{2} \\ $$$${division}\:{euclidienne}\:{par}\:\boldsymbol{\mathrm{x}}^{\mathrm{2}} −\mathrm{1} \\ $$$$ \\ $$

Question Number 186022 Answers: 0 Comments: 5

prove that(using Epsilon−Delta definition) (a) lim_(x→3) ( 2x^2 +1)=19 (b) lim_(x→2) x^3 =8

$${prove}\:\:{that}\left({using}\:{Epsilon}−{Delta}\:{definition}\right) \\ $$$$\left({a}\right)\:\underset{{x}\rightarrow\mathrm{3}} {\mathrm{lim}}\left(\:\mathrm{2}{x}^{\mathrm{2}} +\mathrm{1}\right)=\mathrm{19} \\ $$$$\left({b}\right)\:\underset{{x}\rightarrow\mathrm{2}} {\mathrm{lim}}\:{x}^{\mathrm{3}} =\mathrm{8} \\ $$

Question Number 186021 Answers: 1 Comments: 0

prove that(using Epsilon−Delta definition) (a) lim_(x→1) (6x−2)=4 (b)lim_(x→6) (√(3x−2))=4

$${prove}\:{that}\left({using}\:{Epsilon}−{Delta}\:{definition}\right) \\ $$$$\left({a}\right)\:\underset{{x}\rightarrow\mathrm{1}} {\mathrm{lim}}\left(\mathrm{6}{x}−\mathrm{2}\right)=\mathrm{4} \\ $$$$\left({b}\right)\underset{{x}\rightarrow\mathrm{6}} {\mathrm{lim}}\sqrt{\mathrm{3}{x}−\mathrm{2}}=\mathrm{4} \\ $$

Question Number 186002 Answers: 1 Comments: 1

Question Number 185982 Answers: 1 Comments: 0

Question Number 185981 Answers: 1 Comments: 0

solve in R ⌊ 2x ⌋ + ⌊ 3x ⌋ = 1 ⌊ x ⌋ := greatest integer number more than or equal to ” x ”

$$ \\ $$$$\:\:\:\:\:\:\:{solve}\:\:{in}\:\:\:\mathbb{R} \\ $$$$\: \\ $$$$\:\:\:\:\:\:\:\:\lfloor\:\:\mathrm{2}{x}\:\rfloor\:\:+\:\lfloor\:\:\mathrm{3}{x}\:\rfloor\:=\:\mathrm{1} \\ $$$$\: \\ $$$$\:\:\:\:\lfloor\:{x}\:\rfloor\::=\:{greatest}\:{integer}\:{number} \\ $$$$\:\:\:\:{more}\:{than}\:\:{or}\:{equal}\:\:{to}\:\:''\:{x}\:'' \\ $$

Question Number 185983 Answers: 1 Comments: 0

{ (( f : [ 0 , 1 ] → R)),(( f (x ) = (( 4^( x) )/(2 + 4^( x) )))) :} is given . find the value of the following expression. E = f ((1/(20)) )+ f((( 2)/(20)) )+... +f (((19)/(20))) −f ((1/2) )=?

$$ \\ $$$$\:\:\:\:\:\begin{cases}{\:\:\:{f}\::\:\:\left[\:\:\mathrm{0}\:\:,\:\:\mathrm{1}\:\right]\:\rightarrow\:\mathbb{R}}\\{\:\:\:\:{f}\:\left({x}\:\right)\:=\:\frac{\:\mathrm{4}^{\:{x}} }{\mathrm{2}\:+\:\mathrm{4}^{\:{x}} }}\end{cases} \\ $$$$\:\:\:\:\:\:{is}\:\:{given}\:.\:\:{find}\:{the}\:{value}\:{of} \\ $$$$\:\:\:\:\:\:{the}\:{following}\:{expression}. \\ $$$$\:\:\:\:\:\:\mathrm{E}\:=\:{f}\:\left(\frac{\mathrm{1}}{\mathrm{20}}\:\right)+\:{f}\left(\frac{\:\mathrm{2}}{\mathrm{20}}\:\right)+...\:+{f}\:\left(\frac{\mathrm{19}}{\mathrm{20}}\right)\:−{f}\:\left(\frac{\mathrm{1}}{\mathrm{2}}\:\right)=? \\ $$

Question Number 185973 Answers: 1 Comments: 2

[prove that;] 1 + 2 = 3

$$\:\:\:\:\:\: \\ $$$$\:\:\:\:\:\left[\boldsymbol{{prove}}\:\boldsymbol{{that}};\right] \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{1}\:+\:\mathrm{2}\:=\:\mathrm{3} \\ $$$$ \\ $$

Question Number 185972 Answers: 1 Comments: 0

Question Number 185939 Answers: 0 Comments: 0

Question Number 185901 Answers: 0 Comments: 0

Question Number 185876 Answers: 3 Comments: 0

x = ((2ab)/(a+b)) then prove that ((x + a)/(x − a)) + ((x + b)/(x − b)) = 2

$${x}\:=\:\frac{\mathrm{2}{ab}}{{a}+{b}}\:\mathrm{then}\:\mathrm{prove}\:\mathrm{that}\: \\ $$$$\frac{{x}\:+\:{a}}{{x}\:−\:{a}}\:+\:\frac{{x}\:+\:{b}}{{x}\:−\:{b}}\:=\:\mathrm{2} \\ $$

Question Number 185840 Answers: 0 Comments: 1

Question Number 185843 Answers: 0 Comments: 1

Question Number 185842 Answers: 0 Comments: 1

Question Number 185780 Answers: 0 Comments: 0

find all solutions for k!m!=n! (k,m,n∈N) (m≥k>1)

$${find}\:{all}\:{solutions}\:{for} \\ $$$${k}!{m}!={n}! \\ $$$$\left({k},{m},{n}\in\mathbb{N}\right) \\ $$$$\left({m}\geqslant{k}>\mathrm{1}\right) \\ $$

Question Number 185760 Answers: 1 Comments: 0

A=2×10^0 +10^(−1) +6×10^(−2) +6×10^(−3) +6×10^(−4) +.... (A/(13))=?

$${A}=\mathrm{2}×\mathrm{10}^{\mathrm{0}} +\mathrm{10}^{−\mathrm{1}} +\mathrm{6}×\mathrm{10}^{−\mathrm{2}} +\mathrm{6}×\mathrm{10}^{−\mathrm{3}} +\mathrm{6}×\mathrm{10}^{−\mathrm{4}} +.... \\ $$$$\frac{{A}}{\mathrm{13}}=? \\ $$

Question Number 185747 Answers: 0 Comments: 0

Question Number 185744 Answers: 0 Comments: 0

Question Number 185734 Answers: 4 Comments: 0

x = (√(8 + (√(40 + 8 (√5))))) y = (√(8 − (√(40 + 8 (√5))))) Find: x^6 + y^6 = ?

$$\mathrm{x}\:=\:\sqrt{\mathrm{8}\:+\:\sqrt{\mathrm{40}\:+\:\mathrm{8}\:\sqrt{\mathrm{5}}}} \\ $$$$\mathrm{y}\:=\:\sqrt{\mathrm{8}\:−\:\sqrt{\mathrm{40}\:+\:\mathrm{8}\:\sqrt{\mathrm{5}}}} \\ $$$$\mathrm{Find}:\:\:\:\mathrm{x}^{\mathrm{6}} \:+\:\mathrm{y}^{\mathrm{6}} \:=\:? \\ $$

Question Number 185733 Answers: 0 Comments: 0

Question Number 185723 Answers: 1 Comments: 0

Question Number 185706 Answers: 3 Comments: 0

if x^2 + x + 1 = 0 find: x^(2011) + (1/x^(2011) ) = ?

$$\mathrm{if}\:\:\:\mathrm{x}^{\mathrm{2}} \:+\:\mathrm{x}\:+\:\mathrm{1}\:=\:\mathrm{0} \\ $$$$\mathrm{find}:\:\:\:\:\:\mathrm{x}^{\mathrm{2011}} \:+\:\:\frac{\mathrm{1}}{\mathrm{x}^{\mathrm{2011}} }\:=\:? \\ $$

Question Number 185695 Answers: 2 Comments: 0

If u^→ and v^→ are vectors in R^3 then prove that u^→ .v^→ =(1/4)∥u^→ +v^→ ∥^2 −(1/4)∥u^→ −v^→ ∥^2

$${If}\:\overset{\rightarrow} {{u}}\:{and}\:\overset{\rightarrow} {{v}}\:{are}\:{vectors}\:{in}\:\mathbb{R}^{\mathrm{3}} \\ $$$${then}\:{prove}\:{that}\: \\ $$$$\overset{\rightarrow} {{u}}.\overset{\rightarrow} {{v}}=\frac{\mathrm{1}}{\mathrm{4}}\parallel\overset{\rightarrow} {{u}}+\overset{\rightarrow} {{v}}\parallel^{\mathrm{2}} −\frac{\mathrm{1}}{\mathrm{4}}\parallel\overset{\rightarrow} {{u}}−\overset{\rightarrow} {{v}}\parallel^{\mathrm{2}} \\ $$

Question Number 185694 Answers: 0 Comments: 0

Show that the set V=R^3 with standard vector addition and multiplication defined as c(u_1 ,u_2 ,u_3 )=(0,0,cu_3 )

$${Show}\:{that}\:{the}\:{set}\:{V}=\mathbb{R}^{\mathrm{3}} \:{with} \\ $$$${standard}\:{vector}\:{addition}\:{and} \\ $$$${multiplication}\:{defined}\:{as} \\ $$$${c}\left({u}_{\mathrm{1}} ,{u}_{\mathrm{2}} ,{u}_{\mathrm{3}} \right)=\left(\mathrm{0},\mathrm{0},{cu}_{\mathrm{3}} \right) \\ $$

Pg 81 Pg 82 Pg 83 Pg 84 Pg 85 Pg 86 Pg 87 Pg 88 Pg 89 Pg 90

Contact: info@tinkutara.com