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Question Number 84100    Answers: 2   Comments: 0

Find the differential equations: x(dy/dx)= y− (√(x^2 +y^2 ))

$$\:\mathrm{Find}\:\mathrm{the}\:\mathrm{differential}\:\mathrm{equations}: \\ $$$$\:\:\mathrm{x}\frac{\mathrm{dy}}{\mathrm{dx}}=\:\mathrm{y}−\:\sqrt{\mathrm{x}^{\mathrm{2}} +\mathrm{y}^{\mathrm{2}} } \\ $$

Question Number 84087    Answers: 0   Comments: 1

∫_0 ^3 (√(1+sinh^2 t)) dt

$$\int_{\mathrm{0}} ^{\mathrm{3}} \sqrt{\mathrm{1}+{sinh}^{\mathrm{2}} {t}}\:{dt} \\ $$

Question Number 84085    Answers: 1   Comments: 0

solve (d/dr)(r(dθ/dr))=0

$${solve} \\ $$$$\frac{{d}}{{dr}}\left({r}\frac{{d}\theta}{{dr}}\right)=\mathrm{0} \\ $$

Question Number 84083    Answers: 1   Comments: 3

lim_(a→x) ((((√x) −(√a) −(√(x−a ))))/(√(x^2 −a^2 ))) =

$$\underset{\mathrm{a}\rightarrow\mathrm{x}} {\mathrm{lim}}\:\frac{\left(\sqrt{\mathrm{x}}\:−\sqrt{\mathrm{a}}\:−\sqrt{\mathrm{x}−\mathrm{a}\:}\right)}{\sqrt{\mathrm{x}^{\mathrm{2}} −\mathrm{a}^{\mathrm{2}} }}\:= \\ $$

Question Number 84117    Answers: 2   Comments: 0

Question Number 84068    Answers: 0   Comments: 4

Question Number 84067    Answers: 3   Comments: 0

If lx+my=1 touches the curve (ax)^n +(by)^n =1, show that ((l/a))^(n/(n−1)) +((m/b))^(n/(n−1)) =1.

$$\:\mathrm{If}\:\boldsymbol{{lx}}+\boldsymbol{{my}}=\mathrm{1}\:\mathrm{touches}\:\mathrm{the}\:\mathrm{curve}\:\left(\boldsymbol{\mathrm{ax}}\right)^{\boldsymbol{\mathrm{n}}} +\left(\boldsymbol{\mathrm{by}}\right)^{\boldsymbol{\mathrm{n}}} =\mathrm{1},\:\mathrm{show}\:\mathrm{that} \\ $$$$\:\left(\frac{\boldsymbol{{l}}}{\boldsymbol{{a}}}\right)^{\frac{\boldsymbol{{n}}}{\boldsymbol{{n}}−\mathrm{1}}} +\left(\frac{\boldsymbol{{m}}}{\boldsymbol{{b}}}\right)^{\frac{\boldsymbol{{n}}}{\boldsymbol{{n}}−\mathrm{1}}} =\mathrm{1}. \\ $$

Question Number 84065    Answers: 1   Comments: 2

Determine a and b in order that _(x→0) ^(lim) ((x(1+a cos x)−b sin x )/x^3 )=1.

$$ \\ $$$$\: \\ $$$$\:\boldsymbol{\mathrm{Determine}}\:\boldsymbol{\mathrm{a}}\:\boldsymbol{\mathrm{and}}\:\boldsymbol{\mathrm{b}}\:\boldsymbol{\mathrm{in}}\:\boldsymbol{\mathrm{order}}\:\boldsymbol{\mathrm{that}} \\ $$$$\:\underset{\boldsymbol{\mathrm{x}}\rightarrow\mathrm{0}} {\overset{\boldsymbol{\mathrm{lim}}} {\:}}\:\frac{\boldsymbol{\mathrm{x}}\left(\mathrm{1}+\boldsymbol{\mathrm{a}}\:\boldsymbol{\mathrm{cos}}\:\boldsymbol{\mathrm{x}}\right)−\boldsymbol{\mathrm{b}}\:\boldsymbol{\mathrm{sin}}\:\boldsymbol{\mathrm{x}}\:}{\boldsymbol{\mathrm{x}}^{\mathrm{3}} }=\mathrm{1}. \\ $$

Question Number 84063    Answers: 0   Comments: 0

Find the value of 𝛉 in the Mean Value Theorem f(x+h)=f(x)+h f^( ′) (x+𝛉h) if f(x)= (1/x).

$$ \\ $$$$\:\boldsymbol{\mathrm{Find}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{value}}\:\boldsymbol{\mathrm{of}}\:\boldsymbol{\theta}\:\boldsymbol{\mathrm{in}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{Mean}}\:\boldsymbol{\mathrm{Value}} \\ $$$$\:\boldsymbol{\mathrm{Theorem}}\:\boldsymbol{\mathrm{f}}\left(\boldsymbol{\mathrm{x}}+\boldsymbol{\mathrm{h}}\right)=\boldsymbol{\mathrm{f}}\left(\boldsymbol{\mathrm{x}}\right)+\boldsymbol{\mathrm{h}}\:\boldsymbol{\mathrm{f}}^{\:'} \:\left(\boldsymbol{\mathrm{x}}+\boldsymbol{\theta\mathrm{h}}\right)\:\boldsymbol{\mathrm{if}}\:\boldsymbol{\mathrm{f}}\left(\boldsymbol{\mathrm{x}}\right)=\:\frac{\mathrm{1}}{\boldsymbol{\mathrm{x}}}. \\ $$

Question Number 84059    Answers: 1   Comments: 2

Find (dy/dx) of x^m x^n =(x+y)^(m+n) .

$$ \\ $$$$\:\boldsymbol{\mathrm{Find}}\:\frac{\boldsymbol{\mathrm{dy}}}{\boldsymbol{\mathrm{dx}}}\:\boldsymbol{\mathrm{of}}\:\:\:\boldsymbol{\mathrm{x}}^{\boldsymbol{\mathrm{m}}} \boldsymbol{\mathrm{x}}^{\boldsymbol{\mathrm{n}}} \:=\left(\boldsymbol{\mathrm{x}}+\boldsymbol{\mathrm{y}}\right)^{\boldsymbol{\mathrm{m}}+\boldsymbol{\mathrm{n}}} . \\ $$

Question Number 84213    Answers: 0   Comments: 0

what is the n^(th) derivative of sin^5 (x) by De Moivre′s formula

$$\mathrm{what}\:\mathrm{is}\:\mathrm{the}\:\mathrm{n}^{\mathrm{th}} \: \\ $$$$\mathrm{derivative}\:\mathrm{of}\:\:\mathrm{sin}\:^{\mathrm{5}} \left(\mathrm{x}\right)\:\mathrm{by}\:\mathrm{De}\:\mathrm{Moivre}'\mathrm{s} \\ $$$$\mathrm{formula} \\ $$

Question Number 84212    Answers: 1   Comments: 1

y′ = (2x+3y+1)^2 find the solution

$$\mathrm{y}'\:=\:\left(\mathrm{2x}+\mathrm{3y}+\mathrm{1}\right)^{\mathrm{2}} \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{solution}\: \\ $$

Question Number 84055    Answers: 1   Comments: 1

∫_( 0) ^( 2) ((x^2 +3x)/(√(x+2))) dx = ?

$$\underset{\:\mathrm{0}} {\int}\overset{\:\mathrm{2}} {\:}\:\:\frac{{x}^{\mathrm{2}} +\mathrm{3}{x}}{\sqrt{{x}+\mathrm{2}}}\:\:{dx}\:\:=\:\:? \\ $$

Question Number 84051    Answers: 1   Comments: 0

((log_((x−1)) (6x−1))/(((1/8)(log_3 (x^2 ))^3 −log_3 (x))(log_3 (x−2)−1))) ≥ 0

$$\frac{\mathrm{log}_{\left({x}−\mathrm{1}\right)} \:\left(\mathrm{6}{x}−\mathrm{1}\right)}{\left(\frac{\mathrm{1}}{\mathrm{8}}\left(\mathrm{log}_{\mathrm{3}} \left({x}^{\mathrm{2}} \right)\right)^{\mathrm{3}} −\mathrm{log}_{\mathrm{3}} \:\left({x}\right)\right)\left(\mathrm{log}_{\mathrm{3}} \:\left({x}−\mathrm{2}\right)−\mathrm{1}\right)}\:\geqslant\:\mathrm{0} \\ $$

Question Number 84047    Answers: 2   Comments: 0

how many natural solution are there for x^2 − y ! = 2019 .

$$\mathrm{how}\:\mathrm{many}\: \\ $$$$\mathrm{natural}\:\mathrm{solution}\:\mathrm{are}\:\mathrm{there}\:\mathrm{for}\: \\ $$$${x}^{\mathrm{2}} \:−\:{y}\:!\:=\:\mathrm{2019}\:. \\ $$

Question Number 84046    Answers: 0   Comments: 2

Please any short cut to evaluate: ∫_( 1) ^( 2) (( ((x − x^4 ))^(1/3) )/x^4 )

$$\mathrm{Please}\:\mathrm{any}\:\mathrm{short}\:\mathrm{cut}\:\mathrm{to}\:\mathrm{evaluate}:\:\:\:\:\:\int_{\:\mathrm{1}} ^{\:\mathrm{2}} \:\:\:\frac{\:\:\sqrt[{\mathrm{3}}]{\mathrm{x}\:\:−\:\:\mathrm{x}^{\mathrm{4}} }}{\mathrm{x}^{\mathrm{4}} } \\ $$

Question Number 84039    Answers: 0   Comments: 0

∫((x cos^3 (x))/(sin^5 (x)+cos^5 (x))) dx

$$\int\frac{{x}\:{cos}^{\mathrm{3}} \left({x}\right)}{{sin}^{\mathrm{5}} \left({x}\right)+{cos}^{\mathrm{5}} \left({x}\right)}\:{dx} \\ $$

Question Number 84036    Answers: 1   Comments: 0

∫_(−1) ^(10) sin(x−∣x∣) dx

$$\int_{−\mathrm{1}} ^{\mathrm{10}} {sin}\left({x}−\mid{x}\mid\right)\:{dx} \\ $$

Question Number 84035    Answers: 0   Comments: 2

∫((x−4)/(x^4 −1))dx

$$\int\frac{{x}−\mathrm{4}}{{x}^{\mathrm{4}} −\mathrm{1}}{dx} \\ $$

Question Number 84170    Answers: 2   Comments: 0

∫ (dx/(x^3 ((4−x^3 ))^(1/(3 )) )) ?

$$\int\:\:\frac{\mathrm{dx}}{\mathrm{x}^{\mathrm{3}} \:\:\sqrt[{\mathrm{3}\:\:}]{\mathrm{4}−\mathrm{x}^{\mathrm{3}} }}\:?\: \\ $$

Question Number 84030    Answers: 0   Comments: 0

find ∫ (√((x+2)/(x^2 −x−3)))dx

$${find}\:\int\:\sqrt{\frac{{x}+\mathrm{2}}{{x}^{\mathrm{2}} −{x}−\mathrm{3}}}{dx} \\ $$

Question Number 84029    Answers: 0   Comments: 0

let f(x)=e^(−nx) ln(2+x^2 ) with n integr natural 1) calculste f^((n)) (x) and f^((n)) (0) 2) developp f at integr serie 3)find ∫_0 ^1 f(x)d and ∫_0 ^∞ f(x)dx

$${let}\:{f}\left({x}\right)={e}^{−{nx}} {ln}\left(\mathrm{2}+{x}^{\mathrm{2}} \right)\:\:\:{with}\:{n}\:{integr}\:{natural} \\ $$$$\left.\mathrm{1}\right)\:{calculste}\:{f}^{\left({n}\right)} \left({x}\right)\:{and}\:{f}^{\left({n}\right)} \left(\mathrm{0}\right) \\ $$$$\left.\mathrm{2}\right)\:{developp}\:{f}\:{at}\:{integr}\:{serie} \\ $$$$\left.\mathrm{3}\right){find}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:{f}\left({x}\right){d}\:{and}\:\int_{\mathrm{0}} ^{\infty} {f}\left({x}\right){dx} \\ $$

Question Number 84021    Answers: 3   Comments: 1

Question Number 84019    Answers: 2   Comments: 2

Show that: 1• tan3x=((3−tan^2 x)/(1−3tan^2 x)) using cos3x=4cos^4 x−3cosx sin3x=−4sin^3 x+3sinx Thanks...

$${Show}\:{that}: \\ $$$$\mathrm{1}\bullet\:\:\:{tan}\mathrm{3}{x}=\frac{\mathrm{3}−{tan}^{\mathrm{2}} {x}}{\mathrm{1}−\mathrm{3}{tan}^{\mathrm{2}} {x}} \\ $$$${using}\:{cos}\mathrm{3}{x}=\mathrm{4}{cos}^{\mathrm{4}} {x}−\mathrm{3}{cosx} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{sin}\mathrm{3}{x}=−\mathrm{4}{sin}^{\mathrm{3}} {x}+\mathrm{3}{sinx} \\ $$$${Thanks}... \\ $$

Question Number 84018    Answers: 0   Comments: 0

Question Number 84014    Answers: 0   Comments: 1

find the no. of positivve integral solutions of x+y+2z=89 x>10 y>20 z>2

$${find}\:{the}\:{no}.\:{of}\:{positivve} \\ $$$${integral}\:{solutions}\:{of} \\ $$$${x}+{y}+\mathrm{2}{z}=\mathrm{89} \\ $$$${x}>\mathrm{10} \\ $$$${y}>\mathrm{20} \\ $$$${z}>\mathrm{2} \\ $$

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