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Question Number 187515 Answers: 0 Comments: 0

Given f(x)+2f((1/x))+3f((x/(x−1)))=x f(x)=?

$$\:{Given}\:{f}\left({x}\right)+\mathrm{2}{f}\left(\frac{\mathrm{1}}{{x}}\right)+\mathrm{3}{f}\left(\frac{{x}}{{x}−\mathrm{1}}\right)={x} \\ $$$$\:{f}\left({x}\right)=? \\ $$

Question Number 186103 Answers: 0 Comments: 0

Let R denote a set of all ordered pairs (x, y) of integers such that x−y is an integral multiple of 3. Which of the followings ordered pairs belong to R (9,3) (3, 9),( 1 ,2) (1, 5),(7, 2) (0, 4), (4 ,7). (note: a is an integral multiple of b if a=kb where k is an integer)

$$\mathrm{Let}\:\mathrm{R}\:\mathrm{denote}\:\mathrm{a}\:\mathrm{set}\:\mathrm{of}\:\mathrm{all}\:\mathrm{ordered}\:\mathrm{pairs}\:\left(\mathrm{x},\:\mathrm{y}\right)\: \\ $$$$\mathrm{of}\:\mathrm{integers}\:\mathrm{such}\:\mathrm{that}\:\mathrm{x}−\mathrm{y}\:\mathrm{is}\:\mathrm{an}\:\mathrm{integral} \\ $$$$\:\mathrm{multiple}\:\mathrm{of}\:\mathrm{3}.\:\mathrm{Which}\:\mathrm{of}\:\mathrm{the}\:\mathrm{followings}\:\mathrm{ordered}\:\mathrm{pairs} \\ $$$$\mathrm{belong}\:\mathrm{to}\:\mathrm{R}\:\left(\mathrm{9},\mathrm{3}\right)\:\left(\mathrm{3},\:\mathrm{9}\right),\left(\:\mathrm{1}\:,\mathrm{2}\right)\:\left(\mathrm{1},\:\mathrm{5}\right),\left(\mathrm{7},\:\mathrm{2}\right) \\ $$$$\:\left(\mathrm{0},\:\mathrm{4}\right),\:\left(\mathrm{4}\:,\mathrm{7}\right). \\ $$$$\left(\mathrm{note}:\:\mathrm{a}\:\mathrm{is}\:\mathrm{an}\:\mathrm{integral}\:\mathrm{multiple}\:\mathrm{of}\:\mathrm{b}\:\mathrm{if}\:\mathrm{a}=\mathrm{kb}\right. \\ $$$$\left.\mathrm{whe}{re}\:\mathrm{k}\:\mathrm{is}\:\mathrm{an}\:\mathrm{integer}\right) \\ $$

Question Number 185793 Answers: 2 Comments: 0

Question Number 185678 Answers: 1 Comments: 0

Question Number 185423 Answers: 1 Comments: 0

Σ_(r=1) ^n 3^(r−1) sin^3 ((θ/3^r )) = ?

$$\underset{{r}=\mathrm{1}} {\overset{{n}} {\sum}}\mathrm{3}^{{r}−\mathrm{1}} {sin}^{\mathrm{3}} \left(\frac{\theta}{\mathrm{3}^{{r}} }\right)\:=\:? \\ $$

Question Number 185211 Answers: 3 Comments: 0

Question Number 183712 Answers: 1 Comments: 0

solve: W(In(4x))=(√((x−1)))

$${solve}: \\ $$$${W}\left({In}\left(\mathrm{4}{x}\right)\right)=\sqrt{\left({x}−\mathrm{1}\right)} \\ $$

Question Number 183158 Answers: 1 Comments: 0

Given f(x)= (([(1/3)x]∣2x∣+Ax)/(∣4−x^2 ∣)) if f ′(−1)= 5 then A=? [ ] = floor function

$$\:{Given}\:{f}\left({x}\right)=\:\frac{\left[\frac{\mathrm{1}}{\mathrm{3}}{x}\right]\mid\mathrm{2}{x}\mid+{Ax}}{\mid\mathrm{4}−{x}^{\mathrm{2}} \mid} \\ $$$$\:{if}\:{f}\:'\left(−\mathrm{1}\right)=\:\mathrm{5}\:{then}\:{A}=? \\ $$$$\left[\:\:\:\:\right]\:=\:{floor}\:{function}\: \\ $$

Question Number 183119 Answers: 0 Comments: 0

Question Number 180901 Answers: 1 Comments: 0

∫_1 ^( n) ((⌊x⌋)/x^2 )dx =

$$\int_{\mathrm{1}} ^{\:{n}} \frac{\lfloor{x}\rfloor}{{x}^{\mathrm{2}} }{dx}\:=\: \\ $$

Question Number 178635 Answers: 1 Comments: 2

solution set of log_x^(2 ) ((x/(∣x∣))−x)≥0

$$\mathrm{solution}\:\mathrm{set}\:\mathrm{of}\:\:\mathrm{log}_{\mathrm{x}^{\mathrm{2}\:\:\:} } \left(\frac{\mathrm{x}}{\mid\mathrm{x}\mid}−\mathrm{x}\right)\geqslant\mathrm{0} \\ $$

Question Number 178624 Answers: 1 Comments: 0

let f:[0,1]→ R be given by f(x) = (((1+x^(1/3) )^3 +(1−x^(1/3) )^3 )/(8(1+x))) then max{f(x): x∈[0,1]}−min{f(x):x∈[0,1]} is

Question Number 178032 Answers: 0 Comments: 3

• D={z : ∣z∣<1} • H (A→B) denotes the set of holomorfic functions from A to B • We define: W={f∈H (D→R) : ∣∣f∣∣_W <∞ } where ∣∣ ∙ ∣∣_W : { (W,→,R_+ ),(f, ,(Σ_(n=0) ^∞ ((∣f^((n)) (0)∣)/(n!)))) :} Let f∈W Show that ∀g∈H ( f(D^ )), g○f∈W tip: show that ∣∣h∣∣_W ≤cste × Sup_(z∈D) {∣h(z)∣+∣h′′(z)∣} and that W is an algebra then, re−wright f=f_1 +f_2 with f_2 : z Σ_(n=N) ^∞ ((f^((n)) (0))/(n!))z^n with N great enough to make sure that Σ_(n=0) ^∞ ((g^((n)) (0))/(n!))f_2 ^( n) is well defined and converges over W. ∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙

Question Number 177626 Answers: 3 Comments: 0

Question Number 177146 Answers: 2 Comments: 0

f(x)=f(x−1)+x^2 +2x f(6)=33 faind volue of f(50)=?

$${f}\left({x}\right)={f}\left({x}−\mathrm{1}\right)+{x}^{\mathrm{2}} +\mathrm{2}{x} \\ $$$${f}\left(\mathrm{6}\right)=\mathrm{33}\:\:{faind}\:{volue}\:{of}\:\:{f}\left(\mathrm{50}\right)=? \\ $$

Question Number 176501 Answers: 1 Comments: 1

find the range of x+y such that (x−2)^2 + (y−4)^2 = 49

$$\:\mathrm{find}\:\mathrm{the}\:\mathrm{range}\:\mathrm{of}\:\mathrm{x}+\mathrm{y}\:\mathrm{such}\:\mathrm{that} \\ $$$$\:\left({x}−\mathrm{2}\right)^{\mathrm{2}} +\:\left({y}−\mathrm{4}\right)^{\mathrm{2}} \:=\:\mathrm{49} \\ $$

Question Number 176336 Answers: 2 Comments: 0

in AB_ ^Δ C : ((b−c)/(h_a )) =k , and A^ is given. B^ , C^ =?

$$ \\ $$$$\:{in}\:{A}\overset{\Delta} {{B}}_{\:} {C}\::\:\:\frac{{b}−{c}}{{h}_{{a}} \:}\:={k}\:, \\ $$$$\:\:\:\:\:\:\:\:\:\:{and}\:\:\hat {{A}}\:{is}\:{given}. \\ $$$$\:\:\:\:\:\:\:\:\hat {{B}}\:,\:\hat {{C}}\:=?\:\: \\ $$

Question Number 175863 Answers: 0 Comments: 0

Question Number 175801 Answers: 2 Comments: 5

solve the follwing equation x(√(x )) + y(√(y )) = 3 and x(√(y )) + y(√(x )) = 2 someone solve the above equations in the following way x^3 + y^3 + 2xy(√(xy )) = 9.....(1) and x^2 y + y^2 x + 2xy(√(xy )) = 4......(2) (1) − (2) ⇒ (x − y)(x^2 − y^2 ) = 5 hence x = 3 and y = 2 which is obiviusly does not satisfy the original equations. where is the fallacy in the above solution? Please explain.

$${solve}\:{the}\:{follwing}\:{equation} \\ $$$${x}\sqrt{{x}\:}\:\:\:+\:\:{y}\sqrt{{y}\:}\:\:=\:\:\mathrm{3}\:\:\:{and}\:\:\:{x}\sqrt{{y}\:}\:\:+\:{y}\sqrt{{x}\:}\:\:=\:\:\mathrm{2} \\ $$$${someone}\:{solve}\:{the}\:{above}\:{equations}\:{in}\:{the}\:{following}\:{way}\: \\ $$$${x}^{\mathrm{3}} +\:{y}^{\mathrm{3}} +\:\mathrm{2}{xy}\sqrt{{xy}\:}\:\:=\:\mathrm{9}.....\left(\mathrm{1}\right)\:\:\:\:{and}\:\:\:{x}^{\mathrm{2}} {y}\:\:+\:\:{y}^{\mathrm{2}} {x}\:\:+\:\mathrm{2}{xy}\sqrt{{xy}\:}\:\:=\:\:\mathrm{4}......\left(\mathrm{2}\right) \\ $$$$\left(\mathrm{1}\right)\:−\:\left(\mathrm{2}\right)\:\:\:\Rightarrow\:\:\left({x}\:−\:{y}\right)\left({x}^{\mathrm{2}} \:−\:{y}^{\mathrm{2}} \:\right)\:=\:\mathrm{5} \\ $$$${hence}\:\:{x}\:=\:\mathrm{3}\:\:{and}\:\:{y}\:=\:\mathrm{2}\:\:{which}\:{is}\:{obiviusly}\:{does}\:{not}\:\:{satisfy}\:{the} \\ $$$$\:{original}\:{equations}. \\ $$$${where}\:{is}\:{the}\:{fallacy}\:\:{in}\:{the}\:{above}\:{solution}?\:\:\mathrm{Please}\:\mathrm{explain}. \\ $$

Question Number 175780 Answers: 0 Comments: 0

find the range of the function f(x) = cosx{sinx + (√(sin^2 x + sin^2 α )) }

$$\:\mathrm{find}\:\mathrm{the}\:\mathrm{range}\:\mathrm{of}\:\mathrm{the}\:\mathrm{function} \\ $$$$\:\mathrm{f}\left(\mathrm{x}\right)\:=\:\mathrm{cosx}\left\{\mathrm{sin}{x}\:+\:\sqrt{\mathrm{sin}^{\mathrm{2}} {x}\:+\:\mathrm{sin}^{\mathrm{2}} \alpha\:\:}\:\right\}\:\: \\ $$

Question Number 175674 Answers: 2 Comments: 0