Question and Answers Forum

All Questions   Topic List

AllQuestion and Answers: Page 661

Question Number 146100    Answers: 1   Comments: 1

Question Number 146096    Answers: 1   Comments: 0

Question Number 146090    Answers: 2   Comments: 0

∫_0 ^∞ ((sinh(at)sinh(bt))/(sinh(ct)e^(tz) ))dt= ((ab)/(c(z^2 +c^2 −a^2 −b^2 +K_(k=1) ^∞ ((−4k^2 (k^2 c^2 −a^2 )(k^2 c^2 −b^2 ))/((2k+1)(z^2 +(2k^2 +2k+1)c^2 −a^2 −b^2 ))))))

$$\int_{\mathrm{0}} ^{\infty} \frac{\mathrm{sinh}\left(\mathrm{at}\right)\mathrm{sinh}\left(\mathrm{bt}\right)}{\mathrm{sinh}\left(\mathrm{ct}\right)\mathrm{e}^{\mathrm{tz}} }\mathrm{dt}= \\ $$$$\frac{\mathrm{ab}}{\mathrm{c}\left(\mathrm{z}^{\mathrm{2}} +\mathrm{c}^{\mathrm{2}} −\mathrm{a}^{\mathrm{2}} −\mathrm{b}^{\mathrm{2}} +\underset{\mathrm{k}=\mathrm{1}} {\overset{\infty} {\mathrm{K}}}\frac{−\mathrm{4k}^{\mathrm{2}} \left(\mathrm{k}^{\mathrm{2}} \mathrm{c}^{\mathrm{2}} −\mathrm{a}^{\mathrm{2}} \right)\left(\mathrm{k}^{\mathrm{2}} \mathrm{c}^{\mathrm{2}} −\mathrm{b}^{\mathrm{2}} \right)}{\left(\mathrm{2k}+\mathrm{1}\right)\left(\mathrm{z}^{\mathrm{2}} +\left(\mathrm{2k}^{\mathrm{2}} +\mathrm{2k}+\mathrm{1}\right)\mathrm{c}^{\mathrm{2}} −\mathrm{a}^{\mathrm{2}} −\mathrm{b}^{\mathrm{2}} \right)}\right)} \\ $$

Question Number 146091    Answers: 0   Comments: 0

Question Number 146087    Answers: 1   Comments: 0

1)find U_n =∫_0 ^1 x^n e^(−2x) dx 2)nature of Σ U_n ?

$$\left.\mathrm{1}\right)\mathrm{find}\:\mathrm{U}_{\mathrm{n}} =\int_{\mathrm{0}} ^{\mathrm{1}} \:\mathrm{x}^{\mathrm{n}} \:\mathrm{e}^{−\mathrm{2x}} \:\mathrm{dx} \\ $$$$\left.\mathrm{2}\right)\mathrm{nature}\:\mathrm{of}\:\Sigma\:\mathrm{U}_{\mathrm{n}} ? \\ $$

Question Number 146085    Answers: 0   Comments: 1

f(x,y)=x−(√(x+2y)) 1)condition on x and y to have f symetric 2) find (∂f/∂x) ,(∂f/∂y) ,(∂^2 f/(∂x∂y)) ,(∂^2 f/(∂y∂x)) 3) find (∂^2 f/∂^2 x) and (∂^2 f/∂^2 y)

$$\mathrm{f}\left(\mathrm{x},\mathrm{y}\right)=\mathrm{x}−\sqrt{\mathrm{x}+\mathrm{2y}} \\ $$$$\left.\mathrm{1}\right)\mathrm{condition}\:\mathrm{on}\:\mathrm{x}\:\mathrm{and}\:\mathrm{y}\:\mathrm{to}\:\mathrm{have}\:\mathrm{f}\:\mathrm{symetric} \\ $$$$\left.\mathrm{2}\right)\:\mathrm{find}\:\frac{\partial\mathrm{f}}{\partial\mathrm{x}}\:,\frac{\partial\mathrm{f}}{\partial\mathrm{y}}\:,\frac{\partial^{\mathrm{2}} \mathrm{f}}{\partial\mathrm{x}\partial\mathrm{y}}\:,\frac{\partial^{\mathrm{2}} \mathrm{f}}{\partial\mathrm{y}\partial\mathrm{x}} \\ $$$$\left.\mathrm{3}\right)\:\mathrm{find}\:\frac{\partial^{\mathrm{2}} \mathrm{f}}{\partial^{\mathrm{2}} \mathrm{x}}\:\mathrm{and}\:\frac{\partial^{\mathrm{2}} \mathrm{f}}{\partial^{\mathrm{2}} \mathrm{y}} \\ $$

Question Number 146083    Answers: 1   Comments: 0

F(x)=x^n −e^(inα) 1) roots of F(x)? 2) factorize F(x) inside C[x]

$$\mathrm{F}\left(\mathrm{x}\right)=\mathrm{x}^{\mathrm{n}} \:−\mathrm{e}^{\mathrm{in}\alpha} \\ $$$$\left.\mathrm{1}\right)\:\mathrm{roots}\:\mathrm{of}\:\mathrm{F}\left(\mathrm{x}\right)? \\ $$$$\left.\mathrm{2}\right)\:\mathrm{factorize}\:\mathrm{F}\left(\mathrm{x}\right)\:\mathrm{inside}\:\mathrm{C}\left[\mathrm{x}\right] \\ $$

Question Number 146082    Answers: 0   Comments: 0

p(x)=(x^2 −x+1)^n −(x^2 +x+1)^n 1) roots of p(x)? 2) factorize p(x) inside C[x]

$$\mathrm{p}\left(\mathrm{x}\right)=\left(\mathrm{x}^{\mathrm{2}} −\mathrm{x}+\mathrm{1}\right)^{\mathrm{n}} −\left(\mathrm{x}^{\mathrm{2}} +\mathrm{x}+\mathrm{1}\right)^{\mathrm{n}} \\ $$$$\left.\mathrm{1}\right)\:\mathrm{roots}\:\mathrm{of}\:\mathrm{p}\left(\mathrm{x}\right)? \\ $$$$\left.\mathrm{2}\right)\:\mathrm{factorize}\:\mathrm{p}\left(\mathrm{x}\right)\:\mathrm{inside}\:\mathrm{C}\left[\mathrm{x}\right] \\ $$

Question Number 146076    Answers: 1   Comments: 0

if f(x)=∫(3x^2 −2)dx and f(2)=9 then f(−2)= ?

$${if}\:{f}\left({x}\right)=\int\left(\mathrm{3}{x}^{\mathrm{2}} −\mathrm{2}\right){dx}\:{and}\:{f}\left(\mathrm{2}\right)=\mathrm{9}\:{then} \\ $$$${f}\left(−\mathrm{2}\right)=\:? \\ $$

Question Number 146073    Answers: 0   Comments: 0

Let K be nonempty corps , K^∗ =K−{0_K } Prove that 1) Π_(x∈K^∗ ) x = −1 2)Deduce that p is prime ⇔ (p−1)!≡−1[p]

$${Let}\:{K}\:{be}\:{nonempty}\:\:{corps}\:,\:{K}^{\ast} ={K}−\left\{\mathrm{0}_{{K}} \right\} \\ $$$${Prove}\:{that} \\ $$$$\left.\mathrm{1}\right)\:\underset{{x}\in{K}^{\ast} } {\prod}{x}\:=\:−\mathrm{1} \\ $$$$\left.\mathrm{2}\right){Deduce}\:{that}\: \\ $$$$\:\:{p}\:{is}\:{prime}\:\Leftrightarrow\:\left({p}−\mathrm{1}\right)!\equiv−\mathrm{1}\left[{p}\right] \\ $$

Question Number 146072    Answers: 0   Comments: 0

Let F_n =2^2^n +1 the fermat number Prove that F_n is prime ⇔ 3^((F_n −1)/2) ≡1[F_n ]

$${Let}\:{F}_{{n}} =\mathrm{2}^{\mathrm{2}^{{n}} } +\mathrm{1}\:{the}\:{fermat}\:{number} \\ $$$${Prove}\:{that} \\ $$$$\:{F}_{{n}} \:{is}\:{prime}\:\Leftrightarrow\:\mathrm{3}^{\frac{{F}_{{n}} −\mathrm{1}}{\mathrm{2}}} \equiv\mathrm{1}\left[{F}_{{n}} \right] \\ $$

Question Number 146067    Answers: 1   Comments: 0

transform the cartesian inyegral ∫_0 ^1 ∫_0 ^(√(1−x^2 )) e^(−(x^2 +y^2 )) dy dx into polar integral and evaluate it.

$${transform}\:{the}\:{cartesian}\:{inyegral}\: \\ $$$$\underset{\mathrm{0}} {\overset{\mathrm{1}} {\int}}\:\:\:\underset{\mathrm{0}} {\overset{\sqrt{\mathrm{1}−{x}^{\mathrm{2}} }} {\int}}{e}^{−\left({x}^{\mathrm{2}} +{y}^{\mathrm{2}} \right)} \:{dy}\:{dx}\:{into}\:{polar}\:{integral}\: \\ $$$${and}\:{evaluate}\:{it}. \\ $$

Question Number 146063    Answers: 1   Comments: 0

if g(x)=((x^( 2) −x)/(2x−1)) , D_g = [1 , ∞) , lim_(x→∞) ((g^( −1) (x))/(ax + b)) = b−a (a <0 ) then find the value of Max (b ) D_( g) = Domain

$$ \\ $$$$\:\:\:\:{if}\:\:{g}\left({x}\right)=\frac{{x}^{\:\mathrm{2}} −{x}}{\mathrm{2}{x}−\mathrm{1}}\:\:\:,\:{D}_{{g}} =\:\left[\mathrm{1}\:,\:\infty\right) \\ $$$$\:\:\:\:,\:{lim}_{{x}\rightarrow\infty} \frac{{g}^{\:−\mathrm{1}} \left({x}\right)}{{ax}\:+\:{b}}\:=\:{b}−{a}\:\:\left({a}\:<\mathrm{0}\:\right) \\ $$$$\:\:{then}\:{find}\:\:{the}\:{value}\:{of}\:{Max}\:\left({b}\:\right) \\ $$$$\:\: \\ $$$$\:\:{D}_{\:{g}} \:=\:{Domain}\: \\ $$

Question Number 146062    Answers: 0   Comments: 1

find values a , b , c such that: −1≤ ax^2 +bx +c ≤ 1 and ((6b^( 2) + 8 a^( 2) )/3) is Max...

$$ \\ $$$$\:\:\:\:{find}\:\:{values}\:\:{a}\:,\:{b}\:,\:{c}\:\:{such}\:{that}: \\ $$$$\:\:\:\:−\mathrm{1}\leqslant\:{ax}\:^{\mathrm{2}} +{bx}\:+{c}\:\leqslant\:\mathrm{1} \\ $$$$\:\:\:\:\:\:{and}\:\:\frac{\mathrm{6}{b}^{\:\mathrm{2}} +\:\mathrm{8}\:{a}^{\:\mathrm{2}} }{\mathrm{3}}\:{is}\:{Max}... \\ $$

Question Number 146061    Answers: 0   Comments: 0

Question Number 146057    Answers: 1   Comments: 0

Question Number 146054    Answers: 0   Comments: 0

I := ∫_0 ^( ∞) e^( −x) . J_(1/2) (x ) dx J_(v ) (x ) = x^( v) Σ_(n=0) ^( ∞) (((− 1 )^( n) x^( 2n) )/(2^( n + v) n ! Γ ( n + v +1 ))) ....

$$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\mathrm{I}\::=\:\int_{\mathrm{0}} ^{\:\:\infty} {e}^{\:−{x}} \:.\:\mathrm{J}_{\frac{\mathrm{1}}{\mathrm{2}}} \:\left({x}\:\right)\:{dx} \\ $$$$\:\:\:\:\:\:\:\:\:\:\mathrm{J}_{{v}\:} \:\left({x}\:\right)\:=\:{x}^{\:{v}} \:\underset{{n}=\mathrm{0}} {\overset{\:\infty} {\sum}}\frac{\left(−\:\mathrm{1}\:\right)^{\:{n}} \:{x}^{\:\mathrm{2}{n}} }{\mathrm{2}^{\:{n}\:+\:{v}} \:{n}\:!\:\Gamma\:\left(\:{n}\:+\:{v}\:+\mathrm{1}\:\right)} \\ $$$$\:\:\:.... \\ $$

Question Number 146048    Answers: 1   Comments: 0

in a triangle ABC we have { ((3sinA^ +4cosB^ =6)),((4sinB^ +3cosA^ =1)) :} find C^

$${in}\:{a}\:{triangle}\:{ABC}\:\:{we}\:{have}\: \\ $$$$\begin{cases}{\mathrm{3}{sin}\hat {{A}}+\mathrm{4}{cos}\hat {{B}}=\mathrm{6}}\\{\mathrm{4}{sin}\hat {{B}}+\mathrm{3}{cos}\hat {{A}}=\mathrm{1}}\end{cases} \\ $$$${find}\:\hat {{C}} \\ $$$$ \\ $$

Question Number 146046    Answers: 1   Comments: 0

f(x) = x^(sin(x)) ⇒ f^′ (x) = ?

$${f}\left({x}\right)\:=\:{x}^{\boldsymbol{{sin}}\left(\boldsymbol{{x}}\right)} \:\Rightarrow\:{f}\:^{'} \left({x}\right)\:=\:? \\ $$

Question Number 146043    Answers: 2   Comments: 0

Question Number 146044    Answers: 1   Comments: 0

Simplify: ((sin^3 α)/(1-cosα)) + ((cos^3 α)/(sinα+1)) = ?

$${Simplify}: \\ $$$$\frac{{sin}^{\mathrm{3}} \alpha}{\mathrm{1}-{cos}\alpha}\:+\:\frac{{cos}^{\mathrm{3}} \alpha}{{sin}\alpha+\mathrm{1}}\:=\:? \\ $$

Question Number 146035    Answers: 2   Comments: 0

help me please ∫((ln(x+1))/x)dx=??

$${help}\:{me}\:{please} \\ $$$$\int\frac{{ln}\left({x}+\mathrm{1}\right)}{{x}}{dx}=?? \\ $$$$ \\ $$

Question Number 146030    Answers: 0   Comments: 1

Question Number 146026    Answers: 2   Comments: 3

Question Number 146017    Answers: 1   Comments: 0

Question Number 146013    Answers: 0   Comments: 0

  Pg 656      Pg 657      Pg 658      Pg 659      Pg 660      Pg 661      Pg 662      Pg 663      Pg 664      Pg 665   

Terms of Service

Privacy Policy

Contact: info@tinkutara.com