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Question Number 63108 Answers: 2 Comments: 1

Question Number 63103 Answers: 1 Comments: 2

Question Number 63101 Answers: 3 Comments: 1

calculate S =(1/(1×2)) +(1/(3×4)) +(1/(5×6)) +.....

$${calculate}\:\:{S}\:=\frac{\mathrm{1}}{\mathrm{1}×\mathrm{2}}\:+\frac{\mathrm{1}}{\mathrm{3}×\mathrm{4}}\:+\frac{\mathrm{1}}{\mathrm{5}×\mathrm{6}}\:+..... \\ $$

Question Number 63095 Answers: 1 Comments: 0

Question Number 63090 Answers: 0 Comments: 0

s=(√(a^2 +(a^2 −d)^2 ))+(√((b−a)^2 +(b^2 −a^2 )^2 )) +(√(b^2 +(c−b^2 )^2 ))+c−d p= a(a^2 −d)+(a+b)(b^2 −a^2 ) +b(c−b^2 ) Find a,b,c, or d in terms of s if p is maximum. Assume a,b,c,d ≥0 .

$${s}=\sqrt{{a}^{\mathrm{2}} +\left({a}^{\mathrm{2}} −{d}\right)^{\mathrm{2}} }+\sqrt{\left({b}−{a}\right)^{\mathrm{2}} +\left({b}^{\mathrm{2}} −{a}^{\mathrm{2}} \right)^{\mathrm{2}} } \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:+\sqrt{{b}^{\mathrm{2}} +\left({c}−{b}^{\mathrm{2}} \right)^{\mathrm{2}} }+{c}−{d} \\ $$$$\:{p}=\:{a}\left({a}^{\mathrm{2}} −{d}\right)+\left({a}+{b}\right)\left({b}^{\mathrm{2}} −{a}^{\mathrm{2}} \right) \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:+{b}\left({c}−{b}^{\mathrm{2}} \right) \\ $$$${Find}\:{a},{b},{c},\:{or}\:{d}\:\:{in}\:{terms}\:{of}\:{s} \\ $$$${if}\:\:{p}\:{is}\:{maximum}.\: \\ $$$${Assume}\:\:\:\:{a},{b},{c},{d}\:\geqslant\mathrm{0}\:. \\ $$

Question Number 63089 Answers: 0 Comments: 3

find the value of ∫_0 ^(π/2) (dx/(1+(tanx)^(√2) )) .

$${find}\:{the}\:{value}\:{of}\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:\:\frac{{dx}}{\mathrm{1}+\left({tanx}\right)^{\sqrt{\mathrm{2}}} }\:. \\ $$

Question Number 63084 Answers: 0 Comments: 1

let f(z) =((cos(3z))/z^2 ) calculate Res(f,0) .

$${let}\:{f}\left({z}\right)\:=\frac{{cos}\left(\mathrm{3}{z}\right)}{{z}^{\mathrm{2}} } \\ $$$${calculate}\:{Res}\left({f},\mathrm{0}\right)\:. \\ $$

Question Number 63080 Answers: 0 Comments: 0

∫((√((sinx)/x^3 ))/x^3 )dx

$$\:\int\frac{\sqrt{\frac{{sinx}}{{x}^{\mathrm{3}} }}}{{x}^{\mathrm{3}} }{dx} \\ $$

Question Number 63079 Answers: 0 Comments: 1

let f(z) =((sin(2z))/z^n ) with n integr natural calculate Res(f,0)

$${let}\:{f}\left({z}\right)\:=\frac{{sin}\left(\mathrm{2}{z}\right)}{{z}^{{n}} }\:\:\:\:{with}\:{n}\:{integr}\:{natural}\: \\ $$$${calculate}\:{Res}\left({f},\mathrm{0}\right) \\ $$

Question Number 63073 Answers: 2 Comments: 1

Question Number 63065 Answers: 0 Comments: 3

If I=∫_( 0) ^1 (dx/(√(1+x^4 ))) , then

$$\mathrm{If}\:{I}=\underset{\:\mathrm{0}} {\overset{\mathrm{1}} {\int}}\:\frac{{dx}}{\sqrt{\mathrm{1}+{x}^{\mathrm{4}} }}\:,\:\mathrm{then} \\ $$

Question Number 63076 Answers: 0 Comments: 0

show that f:A→B is bijection then f(A_1 ^c )=[f(A_1 )]^c

$${show}\:{that}\:{f}:{A}\rightarrow{B}\:{is}\:{bijection}\:{then}\:{f}\left({A}_{\mathrm{1}} ^{{c}} \right)=\left[{f}\left({A}_{\mathrm{1}} \right)\right]^{{c}} \\ $$

Question Number 63059 Answers: 0 Comments: 0

Question Number 63054 Answers: 0 Comments: 0

if Σ∣a_n ∣ is convergent, then prove that there exists a subsequence {n_k a_n_k } with lim_(k→∞) n_k a_n_k =0

$${if}\:\Sigma\mid{a}_{{n}} \:\mid\:{is}\:{convergent},\:{then} \\ $$$${prove}\:{that}\:{there}\:{exists}\: \\ $$$${a}\:{subsequence}\:\left\{{n}_{{k}} {a}_{{n}_{{k}} } \right\}\:\:{with} \\ $$$$\underset{{k}\rightarrow\infty} {\mathrm{lim}}{n}_{{k}} {a}_{{n}_{{k}} } =\mathrm{0} \\ $$

Question Number 63034 Answers: 0 Comments: 0

calculate ∫_0 ^(π/2) (ln(cosx))^2 dx

$${calculate}\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \left({ln}\left({cosx}\right)\right)^{\mathrm{2}} \:{dx}\: \\ $$

Question Number 63033 Answers: 0 Comments: 1

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

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

Question Number 63032 Answers: 0 Comments: 1

let f(z) =(1/(sin(πz))) calculate Res(f,n) with n integr

$${let}\:{f}\left({z}\right)\:=\frac{\mathrm{1}}{{sin}\left(\pi{z}\right)}\:\:{calculate}\:{Res}\left({f},{n}\right)\:{with}\:{n}\:{integr} \\ $$

Question Number 63031 Answers: 0 Comments: 2

let f(z) =((sin(z))/z^2 ) calculate Res(f,0)

$${let}\:{f}\left({z}\right)\:=\frac{{sin}\left({z}\right)}{{z}^{\mathrm{2}} }\:\:{calculate}\:{Res}\left({f},\mathrm{0}\right) \\ $$

Question Number 63026 Answers: 0 Comments: 0

calculate ∫_0 ^π ((sin(2x))/(2cosx −3sinx))dx

$${calculate}\:\int_{\mathrm{0}} ^{\pi} \:\:\frac{{sin}\left(\mathrm{2}{x}\right)}{\mathrm{2}{cosx}\:−\mathrm{3}{sinx}}{dx} \\ $$

Question Number 63023 Answers: 0 Comments: 1

calculate ∫_(−∞) ^(+∞) ((x^2 −3)/(x^4 +x^2 +1))dx .

$${calculate}\:\int_{−\infty} ^{+\infty} \:\:\:\frac{{x}^{\mathrm{2}} −\mathrm{3}}{{x}^{\mathrm{4}} \:+{x}^{\mathrm{2}} \:+\mathrm{1}}{dx}\:. \\ $$

Question Number 63021 Answers: 2 Comments: 3

solve this equation x^y =y^x x,y∈R.

$${solve}\:{this}\:{equation} \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{x}^{{y}} ={y}^{{x}} \\ $$$$ \\ $$$$ \\ $$$${x},{y}\in\mathbb{R}. \\ $$

Question Number 63017 Answers: 0 Comments: 0

445x((5x)/)

$$\mathrm{445}\boldsymbol{{x}}\frac{\mathrm{5}\boldsymbol{{x}}}{} \\ $$$$ \\ $$

Question Number 63016 Answers: 1 Comments: 0

The sides of a hexagon are enlarged by three times. Find the ratio of the areas of the new and old hexagon

$$\mathrm{The}\:\mathrm{sides}\:\mathrm{of}\:\mathrm{a}\:\mathrm{hexagon}\:\mathrm{are}\:\mathrm{enlarged}\:\mathrm{by}\: \\ $$$$\mathrm{three}\:\mathrm{times}.\:\mathrm{Find}\:\mathrm{the}\:\mathrm{ratio}\:\mathrm{of}\:\mathrm{the}\:\mathrm{areas} \\ $$$$\mathrm{of}\:\mathrm{the}\:\mathrm{new}\:\mathrm{and}\:\mathrm{old}\:\mathrm{hexagon} \\ $$

Question Number 63015 Answers: 0 Comments: 0

f(x,y,z)= x(p+z)+y(p−z) +((4x^3 )/(p+z))+((4y^3 )/(p−z))+4(x+y)^2 (y−x) ∀ p(x,y)=c+(x−y)(√(1+(x+y)^2 )) +(x^2 −y^2 ) Determine x,y,z such that f is maximum. (c is a constant). Assume y≥x.

$${f}\left({x},{y},{z}\right)=\:{x}\left({p}+{z}\right)+{y}\left({p}−{z}\right) \\ $$$$\:\:\:\:+\frac{\mathrm{4}{x}^{\mathrm{3}} }{{p}+{z}}+\frac{\mathrm{4}{y}^{\mathrm{3}} }{{p}−{z}}+\mathrm{4}\left({x}+{y}\right)^{\mathrm{2}} \left({y}−{x}\right) \\ $$$$\forall\:\:{p}\left({x},{y}\right)={c}+\left({x}−{y}\right)\sqrt{\mathrm{1}+\left({x}+{y}\right)^{\mathrm{2}} } \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:+\left({x}^{\mathrm{2}} −{y}^{\mathrm{2}} \right) \\ $$$${Determine}\:{x},{y},{z}\:{such}\:{that}\:{f}\:{is} \\ $$$${maximum}.\:\left({c}\:{is}\:{a}\:{constant}\right). \\ $$$${Assume}\:{y}\geqslant{x}. \\ $$

Question Number 62998 Answers: 0 Comments: 12

Solve for x: 5^x +6x=7

$${Solve}\:{for}\:{x}:\:\:\mathrm{5}^{\boldsymbol{{x}}} +\mathrm{6}\boldsymbol{{x}}=\mathrm{7} \\ $$

Question Number 62997 Answers: 0 Comments: 1

∫((ln(1+xsin^2 (x)))/(sin^2 (x))) dx

$$\int\frac{{ln}\left(\mathrm{1}+{xsin}^{\mathrm{2}} \left({x}\right)\right)}{{sin}^{\mathrm{2}} \left({x}\right)}\:{dx} \\ $$

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