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Question Number 58587 Answers: 0 Comments: 0

For x > 0 , y < 1 . Prove that x^y + y^x > 1

$${For}\:\:\:{x}\:>\:\mathrm{0}\:\:,\:\:\:{y}\:\:<\:\:\mathrm{1}\:. \\ $$$${Prove}\:\:{that}\:\:\:\:{x}^{{y}} \:+\:{y}^{{x}} \:\:>\:\:\mathrm{1} \\ $$

Question Number 58584 Answers: 0 Comments: 0

((X−λ)/(√(λ/n)))

$$\frac{{X}−\lambda}{\sqrt{\frac{\lambda}{{n}}}} \\ $$

Question Number 58576 Answers: 2 Comments: 0

lim_(x→∞) (((x−20)^(70) .(2x+3)^(30) )/((4x−1)^(15) .(5−x^(85) )))

$$\underset{{x}\rightarrow\infty} {{lim}}\:\:\frac{\left({x}−\mathrm{20}\right)^{\mathrm{70}} .\left(\mathrm{2}{x}+\mathrm{3}\right)^{\mathrm{30}} }{\left(\mathrm{4}{x}−\mathrm{1}\right)^{\mathrm{15}} .\left(\mathrm{5}−{x}^{\mathrm{85}} \right)} \\ $$

Question Number 58569 Answers: 1 Comments: 0

A vector has magnitude 6 and bearing 100°.write it in the form ai+bj

$${A}\:{vector}\:{has}\:{magnitude} \\ $$$$\mathrm{6}\:{and}\:{bearing}\:\mathrm{100}°.{write} \\ $$$${it}\:{in}\:{the}\:{form}\:{ai}+{bj} \\ $$

Question Number 58568 Answers: 2 Comments: 1

factorize px^2 −py^2 +qy^2 −px^2

$${factorize} \\ $$$${px}^{\mathrm{2}} −{py}^{\mathrm{2}} +{qy}^{\mathrm{2}} −{px}^{\mathrm{2}} \\ $$

Question Number 58567 Answers: 0 Comments: 1

A regular polygon of (2k+1) sides has 140 as the size of each interior angle.Find k

$$\:{A}\:{regular}\:{polygon}\:{of}\:\left(\mathrm{2}{k}+\mathrm{1}\right)\:{sides} \\ $$$${has}\:\mathrm{140}\:{as}\:{the}\:{size}\:{of}\:{each}\:{interior} \\ $$$${angle}.{Find}\:{k} \\ $$

Question Number 58547 Answers: 1 Comments: 1

Question Number 58558 Answers: 1 Comments: 0

lim_(x→0) ((√(2x^2 − 2ax + b − 3))/(x ((x^5 + 8))^(1/3) )) = (2/3) Value of ab is ...

$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\:\:\frac{\sqrt{\mathrm{2}{x}^{\mathrm{2}} \:−\:\mathrm{2}{ax}\:+\:{b}\:−\:\mathrm{3}}}{{x}\:\:\sqrt[{\mathrm{3}}]{{x}^{\mathrm{5}} \:+\:\mathrm{8}}}\:\:=\:\:\frac{\mathrm{2}}{\mathrm{3}} \\ $$$${Value}\:\:{of}\:\:\:{ab}\:\:{is}\:\:... \\ $$

Question Number 58530 Answers: 2 Comments: 0

find lim_(x→0) ((1−cos(2x) cos(3x^3 ))/x^2 )

$${find}\:{lim}_{{x}\rightarrow\mathrm{0}} \:\:\frac{\mathrm{1}−{cos}\left(\mathrm{2}{x}\right)\:{cos}\left(\mathrm{3}{x}^{\mathrm{3}} \right)}{{x}^{\mathrm{2}} } \\ $$

Question Number 58521 Answers: 1 Comments: 0

sin 16^° =? cos 16^° =? without using cos(3θ) algebric method please

$$\boldsymbol{{sin}}\:\mathrm{16}^{°} \:=? \\ $$$$\boldsymbol{{cos}}\:\mathrm{16}^{°} \:=? \\ $$$$\boldsymbol{{without}}\:\boldsymbol{{using}}\:\boldsymbol{{cos}}\left(\mathrm{3}\theta\right) \\ $$$$\boldsymbol{{algebric}}\:\boldsymbol{{method}}\:\boldsymbol{{please}} \\ $$

Question Number 58519 Answers: 1 Comments: 1

Question Number 58512 Answers: 1 Comments: 1

Question Number 58508 Answers: 1 Comments: 0

Question Number 58501 Answers: 2 Comments: 0

a and b are roots of this equation : x^(2018) − 2x + 1 = 0 Calculate the value of 2 + (a+b) + (a^2 +b^2 ) + (a^3 + b^3 ) + … + (a^(2017) + b^(2017) )

$${a}\:\:{and}\:\:{b}\:\:{are}\:\:{roots}\:\:{of}\:\:{this}\:\:{equation}\:\:: \\ $$$$\:\:\:\:\:\:\:\:{x}^{\mathrm{2018}} \:−\:\mathrm{2}{x}\:+\:\mathrm{1}\:\:=\:\:\mathrm{0} \\ $$$${Calculate}\:\:{the}\:\:{value}\:\:\:{of} \\ $$$$\:\:\mathrm{2}\:+\:\left({a}+{b}\right)\:+\:\left({a}^{\mathrm{2}} +{b}^{\mathrm{2}} \right)\:+\:\left({a}^{\mathrm{3}} \:+\:{b}^{\mathrm{3}} \right)\:+\:\ldots\:+\:\left({a}^{\mathrm{2017}} \:+\:{b}^{\mathrm{2017}} \right) \\ $$

Question Number 58500 Answers: 2 Comments: 0

change in simplest form : tan^(−1) (((√(1+x^2 ))+(√(1−x^2 )))/((√(1+x^2 ))−(√(1−x^2 ))))

$${change}\:{in}\:{simplest}\:{form}\:: \\ $$$$\mathrm{tan}^{−\mathrm{1}} \frac{\sqrt{\mathrm{1}+{x}^{\mathrm{2}} }+\sqrt{\mathrm{1}−{x}^{\mathrm{2}} }}{\sqrt{\mathrm{1}+{x}^{\mathrm{2}} }−\sqrt{\mathrm{1}−{x}^{\mathrm{2}} }} \\ $$

Question Number 58493 Answers: 1 Comments: 0

Question Number 58488 Answers: 0 Comments: 2

let f(x) =∫ (dt/(x +cost +cos(2t))) (x real) 1) find a explicit form of f(x) 2)determine also ∫ (dt/((x+cost +cos(2t))^2 )) 3) find ∫ (dt/(1+cos(t)+cos(2t))) and ∫ (dt/((3 +cos(t)+cos(2t))^2 ))

$${let}\:{f}\left({x}\right)\:=\int\:\:\:\frac{{dt}}{{x}\:+{cost}\:+{cos}\left(\mathrm{2}{t}\right)}\:\:\left({x}\:{real}\right) \\ $$$$\left.\mathrm{1}\right)\:{find}\:{a}\:{explicit}\:{form}\:{of}\:{f}\left({x}\right) \\ $$$$\left.\mathrm{2}\right){determine}\:{also}\:\int\:\:\frac{{dt}}{\left({x}+{cost}\:+{cos}\left(\mathrm{2}{t}\right)\right)^{\mathrm{2}} } \\ $$$$\left.\mathrm{3}\right)\:{find}\:\int\:\:\:\frac{{dt}}{\mathrm{1}+{cos}\left({t}\right)+{cos}\left(\mathrm{2}{t}\right)}\:{and} \\ $$$$\int\:\:\:\frac{{dt}}{\left(\mathrm{3}\:+{cos}\left({t}\right)+{cos}\left(\mathrm{2}{t}\right)\right)^{\mathrm{2}} } \\ $$

Question Number 58487 Answers: 0 Comments: 3

let f(x) =∫_(π/4) ^(π/3) (dt/(2+xsint)) 1) find a explicit form of f(x) 2)determine also g(x)=∫_(π/4) ^(π/3) ((sint)/((2+xsint)^2 ))dt 3) find the value of ∫_(π/4) ^(π/3) (dt/(2+3sint)) and ∫_(π/4) ^(π/3) ((sint)/((2+3sint)^2 ))dt

$${let}\:{f}\left({x}\right)\:=\int_{\frac{\pi}{\mathrm{4}}} ^{\frac{\pi}{\mathrm{3}}} \:\:\:\frac{{dt}}{\mathrm{2}+{xsint}} \\ $$$$\left.\mathrm{1}\right)\:{find}\:{a}\:{explicit}\:{form}\:{of}\:{f}\left({x}\right) \\ $$$$\left.\mathrm{2}\right){determine}\:{also}\:{g}\left({x}\right)=\int_{\frac{\pi}{\mathrm{4}}} ^{\frac{\pi}{\mathrm{3}}} \:\:\:\frac{{sint}}{\left(\mathrm{2}+{xsint}\right)^{\mathrm{2}} }{dt} \\ $$$$\left.\mathrm{3}\right)\:{find}\:{the}\:{value}\:{of}\:\int_{\frac{\pi}{\mathrm{4}}} ^{\frac{\pi}{\mathrm{3}}} \:\:\frac{{dt}}{\mathrm{2}+\mathrm{3}{sint}} \\ $$$${and}\:\int_{\frac{\pi}{\mathrm{4}}} ^{\frac{\pi}{\mathrm{3}}} \:\:\:\frac{{sint}}{\left(\mathrm{2}+\mathrm{3}{sint}\right)^{\mathrm{2}} }{dt} \\ $$

Question Number 58480 Answers: 0 Comments: 2