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Question Number 161504 Answers: 1 Comments: 0

Montrer a^ partir du crite^ re de Cauchy que U_n =Σ_(k=1) ^n (1/k^2 ) est une de Cauchy. −−−−−−−−−−−−−−−− Show by using Cauchy′s sequence definition that U_n =Σ_(k=1) ^n (1/k^2 ) is a sequence of Cauchy.

$${Montrer}\:\grave {{a}}\:{partir}\:{du}\:{crit}\grave {{e}re}\:{de}\: \\ $$$${Cauchy}\:{que}\:{U}_{{n}} =\underset{{k}=\mathrm{1}} {\overset{{n}} {\sum}}\frac{\mathrm{1}}{{k}^{\mathrm{2}} }\:{est}\:{une} \\ $$$${de}\:{Cauchy}. \\ $$$$−−−−−−−−−−−−−−−− \\ $$$${Show}\:{by}\:{using}\:{Cauchy}'{s}\:{sequence} \\ $$$${definition}\:{that}\:{U}_{{n}} =\underset{{k}=\mathrm{1}} {\overset{{n}} {\sum}}\frac{\mathrm{1}}{{k}^{\mathrm{2}} }\:{is}\:{a}\: \\ $$$${sequence}\:{of}\:{Cauchy}. \\ $$

Question Number 161500 Answers: 1 Comments: 0

x^6 - 6x^5 + ax^4 + bx^3 + cx^2 + dx + 1 = 0 all the roots of the equation are positive find a+b+c+d=?

$$\mathrm{x}^{\mathrm{6}} \:-\:\mathrm{6x}^{\mathrm{5}} \:+\:\mathrm{ax}^{\mathrm{4}} \:+\:\mathrm{bx}^{\mathrm{3}} \:+\:\mathrm{cx}^{\mathrm{2}} \:+\:\mathrm{dx}\:+\:\mathrm{1}\:=\:\mathrm{0} \\ $$$$\mathrm{all}\:\mathrm{the}\:\mathrm{roots}\:\mathrm{of}\:\mathrm{the}\:\mathrm{equation}\:\mathrm{are}\:\mathrm{positive} \\ $$$$\mathrm{find}\:\:\mathrm{a}+\mathrm{b}+\mathrm{c}+\mathrm{d}=? \\ $$

Question Number 161485 Answers: 0 Comments: 0

Find range of function y=((cos 4x+4sin 4x+1)/(cos 4x+2))

$$\:\mathrm{Find}\:\mathrm{range}\:\mathrm{of}\:\mathrm{function}\:\mathrm{y}=\frac{\mathrm{cos}\:\mathrm{4x}+\mathrm{4sin}\:\mathrm{4x}+\mathrm{1}}{\mathrm{cos}\:\mathrm{4x}+\mathrm{2}} \\ $$

Question Number 161484 Answers: 2 Comments: 0

{ (((1/a)+(1/b)=9)),((((1/( (a)^(1/3) ))+(1/( (b)^(1/3) )))(1+(1/( (a)^(1/3) )))(1+(1/( (b)^(1/3) )))=18)) :} 8a+4b=?

$$\:\:\begin{cases}{\frac{\mathrm{1}}{\mathrm{a}}+\frac{\mathrm{1}}{\mathrm{b}}=\mathrm{9}}\\{\left(\frac{\mathrm{1}}{\:\sqrt[{\mathrm{3}}]{\mathrm{a}}}+\frac{\mathrm{1}}{\:\sqrt[{\mathrm{3}}]{\mathrm{b}}}\right)\left(\mathrm{1}+\frac{\mathrm{1}}{\:\sqrt[{\mathrm{3}}]{\mathrm{a}}}\right)\left(\mathrm{1}+\frac{\mathrm{1}}{\:\sqrt[{\mathrm{3}}]{\mathrm{b}}}\right)=\mathrm{18}}\end{cases} \\ $$$$\:\:\:\mathrm{8a}+\mathrm{4b}=? \\ $$

Question Number 161482 Answers: 3 Comments: 1

Question Number 161476 Answers: 0 Comments: 2

Between (3/6) and −(4/5) How do i list two rational numbers please?

$$\:{Between}\:\frac{\mathrm{3}}{\mathrm{6}}\:\:{and}\:−\frac{\mathrm{4}}{\mathrm{5}} \\ $$$$\:{How}\:{do}\:{i}\:{list}\:{two}\:{rational}\: \\ $$$$\:{numbers}\:{please}? \\ $$

Question Number 161538 Answers: 2 Comments: 0

lim_( x → −2 ) (((2+ 3x + 3x^( 2) + x^( 3) )/( sin ( ((πx)/2) ))) )=? −−−−

$$ \\ $$$${lim}_{\:{x}\:\rightarrow\:−\mathrm{2}\:\:} \left(\frac{\mathrm{2}+\:\mathrm{3}{x}\:+\:\mathrm{3}{x}^{\:\mathrm{2}} \:+\:{x}^{\:\mathrm{3}} }{\:{sin}\:\left(\:\frac{\pi{x}}{\mathrm{2}}\:\right)}\:\right)=? \\ $$$$\:\:\:\:−−−− \\ $$

Question Number 161491 Answers: 0 Comments: 0

Question Number 161464 Answers: 0 Comments: 1

Given that in ΔABC, (sin A+sin B):(sin B+sin C):(sin C+sin A)= 6: 4: 5 Find the angle A.

$$\mathrm{Given}\:\mathrm{that}\:\mathrm{in}\:\Delta\mathrm{ABC}, \\ $$$$\left(\mathrm{sin}\:\mathrm{A}+\mathrm{sin}\:\mathrm{B}\right):\left(\mathrm{sin}\:\mathrm{B}+\mathrm{sin}\:\mathrm{C}\right):\left(\mathrm{sin}\:\mathrm{C}+\mathrm{sin}\:\mathrm{A}\right)=\:\mathrm{6}:\:\mathrm{4}:\:\mathrm{5} \\ $$$$\mathrm{Find}\:\mathrm{the}\:\mathrm{angle}\:\mathrm{A}. \\ $$

Question Number 161463 Answers: 2 Comments: 0

Let f(x)= x+∣x∣−1. Find lim_(x→0^+ ) ((f(x)−f(0))/(x−0)) and lim_(x→0^− ) ((f(x)−f(0))/(x−0)). Hence, determine whether f(x) is differentiable at x=0.

$$\mathrm{Let}\:{f}\left({x}\right)=\:{x}+\mid{x}\mid−\mathrm{1}.\: \\ $$$$\mathrm{Find}\:\underset{{x}\rightarrow\mathrm{0}^{+} } {\mathrm{lim}}\:\frac{{f}\left({x}\right)−{f}\left(\mathrm{0}\right)}{{x}−\mathrm{0}}\:\mathrm{and}\:\underset{{x}\rightarrow\mathrm{0}^{−} } {\mathrm{lim}}\:\frac{{f}\left({x}\right)−{f}\left(\mathrm{0}\right)}{{x}−\mathrm{0}}. \\ $$$$\mathrm{Hence},\:\mathrm{determine}\:\mathrm{whether}\:{f}\left({x}\right)\:\mathrm{is}\: \\ $$$$\mathrm{differentiable}\:\mathrm{at}\:{x}=\mathrm{0}. \\ $$

Question Number 161462 Answers: 1 Comments: 0

Find the particular solution to the differential equation 2y′′+5y′+2y=0 subject to the initial conditions y(0)=2y , y′(0)=1 .

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{particular}\:\mathrm{solution}\:\mathrm{to}\:\mathrm{the}\:\mathrm{differential} \\ $$$$\mathrm{equation}\:\mathrm{2}{y}''+\mathrm{5}{y}'+\mathrm{2}{y}=\mathrm{0}\:\mathrm{subject}\:\mathrm{to}\:\mathrm{the}\:\mathrm{initial} \\ $$$$\mathrm{conditions}\:\:{y}\left(\mathrm{0}\right)=\mathrm{2}{y}\:,\:\:{y}'\left(\mathrm{0}\right)=\mathrm{1}\:. \\ $$

Question Number 161461 Answers: 0 Comments: 3

Let the region bounded by the curve y=x(1−x) and the x-axis be R. The line y=mx divides R into two parts, find the value of (1−m)^3 .

$$\mathrm{Let}\:\mathrm{the}\:\mathrm{region}\:\mathrm{bounded}\:\mathrm{by}\:\mathrm{the}\:\mathrm{curve}\: \\ $$$${y}={x}\left(\mathrm{1}−{x}\right)\:\mathrm{and}\:\mathrm{the}\:{x}-\mathrm{axis}\:\mathrm{be}\:\mathrm{R}. \\ $$$$\mathrm{The}\:\mathrm{line}\:{y}={mx}\:\mathrm{divides}\:\mathrm{R}\:\mathrm{into}\:\mathrm{two}\:\mathrm{parts}, \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\left(\mathrm{1}−{m}\right)^{\mathrm{3}} . \\ $$

Question Number 161456 Answers: 0 Comments: 0