Question and Answers Forum

AllQuestion and Answers: Page 1411

Question Number 68956 Answers: 0 Comments: 0

Question Number 68952 Answers: 1 Comments: 0

Question Number 68947 Answers: 0 Comments: 0

please utilise cette fonction to show that N∗N is denombrable f:N⊛N→N (x,y)∣→(((x+y)(x+y+1))/2)+y montrer que f est bijective Please help

$$\mathrm{please} \\ $$$$\mathrm{utilise}\:\mathrm{cette}\:\mathrm{fonction}\:\mathrm{to}\: \\ $$$$\mathrm{sh}\boldsymbol{\mathrm{ow}}\:\boldsymbol{\mathrm{that}}\:\boldsymbol{\mathrm{N}}\ast\boldsymbol{\mathrm{N}}\:\boldsymbol{\mathrm{is}}\:\boldsymbol{\mathrm{denombrable}} \\ $$$$\:\mathrm{f}:\boldsymbol{\mathrm{N}}\circledast\boldsymbol{\mathrm{N}}\rightarrow\boldsymbol{\mathrm{N}} \\ $$$$\:\:\:\:\left(\mathrm{x},\mathrm{y}\right)\shortmid\rightarrow\frac{\left(\mathrm{x}+\mathrm{y}\right)\left(\mathrm{x}+\mathrm{y}+\mathrm{1}\right)}{\mathrm{2}}+\mathrm{y} \\ $$$$\mathrm{montrer}\:\mathrm{que}\:\mathrm{f}\:\mathrm{est}\:\mathrm{bijective} \\ $$$$\:\:\:\boldsymbol{\mathrm{P}}\mathrm{lease}\:\mathrm{help} \\ $$$$ \\ $$$$\:\:\:\:\:\: \\ $$

Question Number 68946 Answers: 0 Comments: 1

Question Number 68941 Answers: 3 Comments: 3

Question Number 68935 Answers: 2 Comments: 0

Find all values for x: (x^2 −7x+11)^(x^2 −13x+42) =1 (Easy)

$${Find}\:{all}\:{values}\:{for}\:\boldsymbol{{x}}: \\ $$$$\left({x}^{\mathrm{2}} −\mathrm{7}{x}+\mathrm{11}\right)^{{x}^{\mathrm{2}} −\mathrm{13}{x}+\mathrm{42}} =\mathrm{1} \\ $$$$\left({Easy}\right) \\ $$

Question Number 68930 Answers: 0 Comments: 3

In the figure we have 7 circles having the same radius. Determine the ratio between the perimeter of one of the circle and the perimeter of the gray region.

$$\mathrm{In}\:\mathrm{the}\:\mathrm{figure}\:\mathrm{we}\:\mathrm{have}\:\mathrm{7}\:\mathrm{circles}\:\mathrm{having} \\ $$$$\mathrm{the}\:\mathrm{same}\:\mathrm{radius}.\:\mathrm{Determine}\:\mathrm{the}\:\mathrm{ratio} \\ $$$$\mathrm{between}\:\mathrm{the}\:\mathrm{perimeter}\:\mathrm{of}\:\mathrm{one}\:\mathrm{of}\:\mathrm{the} \\ $$$$\mathrm{circle}\:\mathrm{and}\:\mathrm{the}\:\mathrm{perimeter}\:\mathrm{of}\:\mathrm{the}\:\mathrm{gray}\:\mathrm{region}. \\ $$

Question Number 68926 Answers: 0 Comments: 0

Question Number 68925 Answers: 0 Comments: 2

Question Number 68924 Answers: 0 Comments: 0

Question Number 68923 Answers: 0 Comments: 2

Question Number 68912 Answers: 1 Comments: 0

Question Number 68899 Answers: 0 Comments: 9

solve for x and y the equation 2lnx −lny =ln(5x−6y)

$${solve}\:{for}\:{x}\:{and}\:{y}\:{the}\:{equation} \\ $$$$\:\mathrm{2}{lnx}\:−{lny}\:={ln}\left(\mathrm{5}{x}−\mathrm{6}{y}\right) \\ $$

Question Number 68898 Answers: 0 Comments: 7

solve for x the equation log_x e^(2x) = eln x −e

$${solve}\:{for}\:{x}\:{the}\:{equation} \\ $$$$\:\:{log}_{{x}} {e}^{\mathrm{2}{x}} \:=\:{eln}\:{x}\:−{e} \\ $$

Question Number 68885 Answers: 0 Comments: 2

if f(x)=((∣x∣)/x) g(x)=x^2 −1 find lim_(x→1) f(g(x))

$${if}\: \\ $$$${f}\left({x}\right)=\frac{\mid{x}\mid}{{x}} \\ $$$${g}\left({x}\right)={x}^{\mathrm{2}} −\mathrm{1} \\ $$$$ \\ $$$${find}\: \\ $$$$ \\ $$$$\underset{{x}\rightarrow\mathrm{1}} {{lim}}\:\:{f}\left({g}\left({x}\right)\right) \\ $$

Question Number 68879 Answers: 0 Comments: 2

let I =∫_0 ^1 (x/(ln(1+x)))dx determine a approximate value of I

$${let}\:{I}\:=\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\frac{{x}}{{ln}\left(\mathrm{1}+{x}\right)}{dx}\:\:{determine}\:{a}\:{approximate}\:{value}\:{of}\:{I} \\ $$

Question Number 68878 Answers: 0 Comments: 0

find ∫((2(√x)+1)/(x^2 +1−(√(x^2 +1))))dx

$${find}\:\int\frac{\mathrm{2}\sqrt{{x}}+\mathrm{1}}{{x}^{\mathrm{2}} +\mathrm{1}−\sqrt{{x}^{\mathrm{2}} +\mathrm{1}}}{dx} \\ $$

Question Number 68877 Answers: 0 Comments: 1

calculate ∫_(−∞) ^(+∞) ((xdx)/((x^2 −x+i)^2 )) with i^2 =−1

$${calculate}\:\int_{−\infty} ^{+\infty} \:\:\:\frac{{xdx}}{\left({x}^{\mathrm{2}} −{x}+{i}\right)^{\mathrm{2}} }\:\:\:\:\:{with}\:{i}^{\mathrm{2}} =−\mathrm{1} \\ $$

Question Number 68876 Answers: 0 Comments: 2

calculate ∫_0 ^∞ (((−1)^x )/((3+x^2 )^2 ))dx

$${calculate}\:\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{\left(−\mathrm{1}\right)^{{x}} }{\left(\mathrm{3}+{x}^{\mathrm{2}} \right)^{\mathrm{2}} }{dx} \\ $$

Question Number 68874 Answers: 0 Comments: 1

calculate ∫_0 ^(2π) (dx/(1+cosx +3sinx))

$${calculate}\:\int_{\mathrm{0}} ^{\mathrm{2}\pi} \:\:\:\frac{{dx}}{\mathrm{1}+{cosx}\:+\mathrm{3}{sinx}} \\ $$

Question Number 68873 Answers: 0 Comments: 1

solve (x^3 +1)y^′ +(2x+3)y =x cos(2x)

$${solve}\:\:\:\left({x}^{\mathrm{3}} +\mathrm{1}\right){y}^{'} \:+\left(\mathrm{2}{x}+\mathrm{3}\right){y}\:={x}\:{cos}\left(\mathrm{2}{x}\right) \\ $$

Question Number 68872 Answers: 0 Comments: 0

solve (x^3 +1)y^′ +(2x+3)y =x cos(2x)

$${solve}\:\:\:\left({x}^{\mathrm{3}} +\mathrm{1}\right){y}^{'} \:+\left(\mathrm{2}{x}+\mathrm{3}\right){y}\:={x}\:{cos}\left(\mathrm{2}{x}\right) \\ $$

Question Number 68871 Answers: 0 Comments: 0

let f(x)=e^(−arctan((2/(√(x^2 +1))))) 1)calculate f^′ (x) 2)give the equation of tangente to graph C_f at point A(1,f(1))

$${let}\:{f}\left({x}\right)={e}^{−{arctan}\left(\frac{\mathrm{2}}{\sqrt{{x}^{\mathrm{2}} +\mathrm{1}}}\right)} \:\: \\ $$$$\left.\mathrm{1}\right){calculate}\:{f}^{'} \left({x}\right) \\ $$$$\left.\mathrm{2}\right){give}\:{the}\:{equation}\:{of}\:{tangente}\:{to}\:{graph}\:{C}_{{f}} {at}\:{point}\:{A}\left(\mathrm{1},{f}\left(\mathrm{1}\right)\right) \\ $$

Question Number 68870 Answers: 0 Comments: 0

let ∣a∣<1 calculate ∫_0 ^1 ln(x)ln(1−ax)ln(1−ax^2 )dx

$${let}\:\:\mid{a}\mid<\mathrm{1}\:\:\:{calculate}\:\int_{\mathrm{0}} ^{\mathrm{1}} {ln}\left({x}\right){ln}\left(\mathrm{1}−{ax}\right){ln}\left(\mathrm{1}−{ax}^{\mathrm{2}} \right){dx} \\ $$

Question Number 68869 Answers: 0 Comments: 0

let f(a) =∫_0 ^(π/2) (dx/(a+sinx)) (a real) 1)find a explicit form for f(a) 2) calculste also g(a)=∫_0 ^(π/2) (dx/((a+sinx)^2 )) and h(a)=∫_0 ^(π/2) (dx/((a+sinx)^3 )) 3)give f^((n)) (a) at form of integral 4) find the values of integrals ∫_0 ^(π/2) (dx/(3+sinx)) , ∫_0 ^(π/2) (dx/((3+sinx)^2 )) and ∫_0 ^(π/2) (dx/((3+sinx)^3 ))

$${let}\:{f}\left({a}\right)\:=\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:\:\frac{{dx}}{{a}+{sinx}}\:\:\:\:\:\left({a}\:{real}\right) \\ $$$$\left.\mathrm{1}\right){find}\:{a}\:{explicit}\:{form}\:\:{for}\:{f}\left({a}\right) \\ $$$$\left.\mathrm{2}\right)\:{calculste}\:{also}\:{g}\left({a}\right)=\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:\:\frac{{dx}}{\left({a}+{sinx}\right)^{\mathrm{2}} }\:\:{and}\:{h}\left({a}\right)=\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:\frac{{dx}}{\left({a}+{sinx}\right)^{\mathrm{3}} } \\ $$$$\left.\mathrm{3}\right){give}\:{f}^{\left({n}\right)} \left({a}\right)\:{at}\:{form}\:{of}\:{integral} \\ $$$$\left.\mathrm{4}\right)\:{find}\:{the}\:{values}\:{of}\:{integrals}\:\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:\:\frac{{dx}}{\mathrm{3}+{sinx}}\:,\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:\:\frac{{dx}}{\left(\mathrm{3}+{sinx}\right)^{\mathrm{2}} } \\ $$$${and}\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:\:\frac{{dx}}{\left(\mathrm{3}+{sinx}\right)^{\mathrm{3}} } \\ $$

Question Number 68868 Answers: 0 Comments: 1

find ∫ (dx/(a+cosx)) with a>0

$${find}\:\int\:\:\:\:\frac{{dx}}{{a}+{cosx}}\:\:{with}\:{a}>\mathrm{0} \\ $$

Pg 1406 Pg 1407 Pg 1408 Pg 1409 Pg 1410 Pg 1411 Pg 1412 Pg 1413 Pg 1414 Pg 1415

Contact: info@tinkutara.com