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Question Number 87464 Answers: 0 Comments: 2

x + (√y) = 7 (√x) + y = 11 find x and y

$$\mathrm{x}\:+\:\sqrt{\mathrm{y}}\:=\:\mathrm{7} \\ $$$$\sqrt{\mathrm{x}}\:+\:\mathrm{y}\:=\:\mathrm{11}\: \\ $$$$\mathrm{find}\:\mathrm{x}\:\mathrm{and}\:\mathrm{y}\: \\ $$

Question Number 87462 Answers: 0 Comments: 7

Calculate lim_(x→1) f(x)=((sin(x−1))/(3x−3)) please detail sirs

$$\mathrm{Calculate}\:\:\:\:\:\:\:\:\mathrm{li}\underset{\mathrm{x}\rightarrow\mathrm{1}} {\mathrm{m}f}\left({x}\right)=\frac{{sin}\left({x}−\mathrm{1}\right)}{\mathrm{3}{x}−\mathrm{3}} \\ $$$${please}\:{detail}\:{sirs} \\ $$

Question Number 87461 Answers: 1 Comments: 1

∫_e^(-1) ^e ((√(1−(lnx)^2 ))/x) dx

$$\underset{{e}^{-\mathrm{1}} } {\overset{\mathrm{e}} {\int}}\:\frac{\sqrt{\mathrm{1}−\left(\mathrm{ln}{x}\right)^{\mathrm{2}} }}{{x}}\:{dx} \\ $$

Question Number 87459 Answers: 0 Comments: 0

find all functions f :R →R so that (x−y)f(x+y) −(x+y) f(x−y) = 4xy (x^2 −y^2 ) ∀x,y ∈R

$$\mathrm{find}\:\mathrm{all}\:\mathrm{functions}\:\mathrm{f}\::\mathbb{R}\:\rightarrow\mathbb{R} \\ $$$$\mathrm{so}\:\mathrm{that}\:\left(\mathrm{x}−\mathrm{y}\right)\mathrm{f}\left(\mathrm{x}+\mathrm{y}\right)\:−\left(\mathrm{x}+\mathrm{y}\right)\:\mathrm{f}\left(\mathrm{x}−\mathrm{y}\right)\:= \\ $$$$\mathrm{4xy}\:\left(\mathrm{x}^{\mathrm{2}} −\mathrm{y}^{\mathrm{2}} \right)\:\forall\mathrm{x},\mathrm{y}\:\in\mathbb{R} \\ $$

Question Number 87439 Answers: 0 Comments: 2

{ ((2^x .3^y =6)),((3^x .4^y =12)) :}

$$\begin{cases}{\mathrm{2}^{\mathrm{x}} .\mathrm{3}^{\mathrm{y}} =\mathrm{6}}\\{\mathrm{3}^{\mathrm{x}} .\mathrm{4}^{\mathrm{y}} =\mathrm{12}}\end{cases} \\ $$

Question Number 87424 Answers: 1 Comments: 5

prove that ((sin x − 2 sin x + sin 3x)/(sin x + 2sin x + sin 3x)) ≡ −tan^2 ((x/2))

$$\mathrm{prove}\:\mathrm{that}\:\:\:\frac{\mathrm{sin}\:{x}\:−\:\mathrm{2}\:\mathrm{sin}\:{x}\:+\:\mathrm{sin}\:\mathrm{3}{x}}{\mathrm{sin}\:{x}\:+\:\mathrm{2sin}\:{x}\:+\:\mathrm{sin}\:\mathrm{3}{x}}\:\equiv\:−\mathrm{tan}^{\mathrm{2}} \left(\frac{{x}}{\mathrm{2}}\right) \\ $$

Question Number 87419 Answers: 1 Comments: 6

if equation sin x + sec x −2tan x −1 = 0 has roots x_1 & x_2 , then the possible value of sin x_1 −cos x_2 ? (a) 4/5 (b) 3/4 (c) 4/3 (d) 3/2 (e) 2

$$\mathrm{if}\:\mathrm{equation}\:\mathrm{sin}\:\mathrm{x}\:+\:\mathrm{sec}\:\mathrm{x}\:−\mathrm{2tan}\:\mathrm{x}\:−\mathrm{1}\:=\:\mathrm{0} \\ $$$$\mathrm{has}\:\mathrm{roots}\:\mathrm{x}_{\mathrm{1}} \:\&\:\mathrm{x}_{\mathrm{2}} \:,\:\mathrm{then}\:\mathrm{the}\: \\ $$$$\mathrm{possible}\:\mathrm{value}\:\mathrm{of}\:\mathrm{sin}\:\mathrm{x}_{\mathrm{1}} −\mathrm{cos}\:\mathrm{x}_{\mathrm{2}} \:? \\ $$$$\left(\mathrm{a}\right)\:\mathrm{4}/\mathrm{5}\:\:\:\:\:\left(\mathrm{b}\right)\:\mathrm{3}/\mathrm{4}\:\:\:\:\:\left(\mathrm{c}\right)\:\mathrm{4}/\mathrm{3}\: \\ $$$$\left(\mathrm{d}\right)\:\mathrm{3}/\mathrm{2}\:\:\:\:\left(\mathrm{e}\right)\:\mathrm{2} \\ $$

Question Number 87418 Answers: 1 Comments: 0

Question Number 87409 Answers: 1 Comments: 2

∫(sinx)^(1/5) dx

$$\int\left({sinx}\right)^{\frac{\mathrm{1}}{\mathrm{5}}} {dx} \\ $$

Question Number 87413 Answers: 1 Comments: 1

Question Number 87398 Answers: 0 Comments: 5

dear mr w a_(n+2) = a_(n+1) − a_n find a_n

$$\mathrm{dear}\:\mathrm{mr}\:\mathrm{w} \\ $$$$\mathrm{a}_{\mathrm{n}+\mathrm{2}} \:=\:\mathrm{a}_{\mathrm{n}+\mathrm{1}} \:−\:\mathrm{a}_{\mathrm{n}} \\ $$$$\mathrm{find}\:\mathrm{a}_{\mathrm{n}} \\ $$

Question Number 87376 Answers: 1 Comments: 0

Question Number 87382 Answers: 1 Comments: 0

Show that tan((5π)/(12)) is a solution of this equation: x^3 −3x^2 −3x+1=0

$$\mathrm{Show}\:\mathrm{that}\:\mathrm{tan}\frac{\mathrm{5}\pi}{\mathrm{12}}\:\:\mathrm{is}\:\mathrm{a}\:\mathrm{solution}\:\mathrm{of}\:\mathrm{this}\: \\ $$$$\mathrm{equation}:\:{x}^{\mathrm{3}} −\mathrm{3}{x}^{\mathrm{2}} −\mathrm{3}{x}+\mathrm{1}=\mathrm{0} \\ $$

Question Number 87379 Answers: 1 Comments: 2

Π_(k = 2) ^(2010) ((k^2 −1)/k^2 ) = ?

$$\underset{\mathrm{k}\:=\:\mathrm{2}} {\overset{\mathrm{2010}} {\prod}}\:\frac{\mathrm{k}^{\mathrm{2}} −\mathrm{1}}{\mathrm{k}^{\mathrm{2}} }\:=\:? \\ $$

Question Number 87378 Answers: 1 Comments: 1

lim_(x→0) ((tan 3x−3tan x)/x^3 )

$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{tan}\:\mathrm{3x}−\mathrm{3tan}\:\mathrm{x}}{\mathrm{x}^{\mathrm{3}} } \\ $$

Question Number 87371 Answers: 1 Comments: 3

∫((x^7 +x^3 +4)/(x^8 −x^5 +9))dx

$$\int\frac{{x}^{\mathrm{7}} +{x}^{\mathrm{3}} +\mathrm{4}}{{x}^{\mathrm{8}} −{x}^{\mathrm{5}} +\mathrm{9}}{dx} \\ $$

Question Number 87369 Answers: 1 Comments: 4

Question Number 87358 Answers: 0 Comments: 0

what is the number of integral values of y for which? lim_(x→0) ((y^2 +10y−24 sin ((1/x)))/(y^2 +10y −24 sin ((2/x)))) does not exist

$$\mathrm{what}\:\mathrm{is}\:\mathrm{the}\:\mathrm{number}\:\mathrm{of}\: \\ $$$$\mathrm{integral}\:\mathrm{values}\:\mathrm{of}\:\mathrm{y}\:\mathrm{for}\:\mathrm{which}? \\ $$$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{y}^{\mathrm{2}} +\mathrm{10y}−\mathrm{24}\:\mathrm{sin}\:\left(\frac{\mathrm{1}}{\mathrm{x}}\right)}{\mathrm{y}^{\mathrm{2}} +\mathrm{10y}\:−\mathrm{24}\:\mathrm{sin}\:\left(\frac{\mathrm{2}}{\mathrm{x}}\right)}\: \\ $$$$\mathrm{does}\:\mathrm{not}\:\mathrm{exist} \\ $$

Question Number 87352 Answers: 1 Comments: 6

f(x)= f(x+1) −x f(0)= 123 f(29) =?

$$\mathrm{f}\left(\mathrm{x}\right)=\:\mathrm{f}\left(\mathrm{x}+\mathrm{1}\right)\:−\mathrm{x} \\ $$$$\mathrm{f}\left(\mathrm{0}\right)=\:\mathrm{123} \\ $$$$\mathrm{f}\left(\mathrm{29}\right)\:=? \\ $$

Question Number 87340 Answers: 3 Comments: 3

∫ ((cos x)/((5+4cos x)^2 )) dx =

$$\int\:\frac{\mathrm{cos}\:\mathrm{x}}{\left(\mathrm{5}+\mathrm{4cos}\:\mathrm{x}\right)^{\mathrm{2}} }\:\mathrm{dx}\:= \\ $$

Question Number 87335 Answers: 1 Comments: 0

Question Number 87325 Answers: 1 Comments: 3

1) ∫e^(√x) dx 2)∫((√(sin(x)))/((√(sin(x)))+(√(cos(x)))))dx

$$\left.\mathrm{1}\right)\:\int{e}^{\sqrt{{x}}} \:{dx} \\ $$$$\left.\mathrm{2}\right)\int\frac{\sqrt{{sin}\left({x}\right)}}{\sqrt{{sin}\left({x}\right)}+\sqrt{{cos}\left({x}\right)}}{dx} \\ $$

Question Number 87322 Answers: 0 Comments: 0

Investigate the stationary value of (x^3 /(1+x^2 )) and sketch the graph

$$\mathrm{I}{nvestigate}\:{the}\:{stationary} \\ $$$${value}\:{of} \\ $$$$\frac{{x}^{\mathrm{3}} }{\mathrm{1}+{x}^{\mathrm{2}} }\:{and}\:{sketch}\:{the}\:{graph} \\ $$

Question Number 87321 Answers: 0 Comments: 0

Question Number 87316 Answers: 0 Comments: 0

Question Number 87313 Answers: 1 Comments: 4

a,b,c=1,2,3,...,n find Σ_(a≠b≠c) abc

$${a},{b},{c}=\mathrm{1},\mathrm{2},\mathrm{3},...,{n} \\ $$$${find}\:\underset{{a}\neq{b}\neq{c}} {\sum}{abc} \\ $$

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