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AllQuestion and Answers: Page 179

Question Number 204372 Answers: 2 Comments: 0

If , f : [ 0 , b] →^(continuous) R , g : R →_(b−periodic) ^(continuous) R ⇒ lim_(n→∞) ∫_0 ^( b) f(x)g(nx)dx=^? (1/b) ∫_0 ^( b) f(x)dx .∫_0 ^( b) g(x)dx

$$ \\ $$$$\:\:{If}\:,\:\:\:\:{f}\::\:\left[\:\mathrm{0}\:,\:{b}\right]\:\overset{{continuous}} {\rightarrow}\:\mathbb{R}\: \\ $$$$\:\:\:\:\:\:\:\:,\:\:\:\:{g}\::\:\mathbb{R}\:\underset{{b}−{periodic}} {\overset{{continuous}} {\rightarrow}}\:\mathbb{R} \\ $$$$\:\:\:\:\:\:\Rightarrow\:\:{lim}_{{n}\rightarrow\infty} \:\int_{\mathrm{0}} ^{\:{b}} {f}\left({x}\right){g}\left({nx}\right){dx}\overset{?} {=}\frac{\mathrm{1}}{{b}}\:\int_{\mathrm{0}} ^{\:{b}} {f}\left({x}\right){dx}\:.\int_{\mathrm{0}} ^{\:{b}} {g}\left({x}\right){dx} \\ $$$$ \\ $$

Question Number 204384 Answers: 0 Comments: 1

Question Number 204360 Answers: 3 Comments: 0

if lim_(x→+∞) [(((a+6)x+1)/(ax+1))]=2→ find the largest and smallest correct value for a.

$${if} \\ $$$$\underset{{x}\rightarrow+\infty} {\mathrm{lim}}\left[\frac{\left({a}+\mathrm{6}\right){x}+\mathrm{1}}{{ax}+\mathrm{1}}\right]=\mathrm{2}\rightarrow \\ $$$${find}\:{the}\:{largest}\:{and}\:{smallest}\:{correct} \\ $$$${value}\:{for}\:{a}. \\ $$

Question Number 204350 Answers: 1 Comments: 0

Question Number 204349 Answers: 1 Comments: 2

Question Number 204348 Answers: 1 Comments: 0

3×7×11 + 7×11×15 + 11×15×19 + ..........+ 39×43×47 = ?

$$\mathrm{3}×\mathrm{7}×\mathrm{11}\:+\:\mathrm{7}×\mathrm{11}×\mathrm{15}\:+\:\mathrm{11}×\mathrm{15}×\mathrm{19}\:+\:..........+\:\:\mathrm{39}×\mathrm{43}×\mathrm{47}\:=\:?\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\: \\ $$

Question Number 204346 Answers: 0 Comments: 0

Question Number 204344 Answers: 1 Comments: 2

ctg^6 ((π/9))−9∙ctg^4 ((π/9))+11∙ctg^2 ((π/9))=?

$$ \\ $$$$\: \\ $$$$ \\ $$$$ \\ $$$$\:\:\:\boldsymbol{\mathrm{ctg}}^{\mathrm{6}} \left(\frac{\pi}{\mathrm{9}}\right)−\mathrm{9}\centerdot\boldsymbol{\mathrm{ctg}}^{\mathrm{4}} \left(\frac{\pi}{\mathrm{9}}\right)+\mathrm{11}\centerdot\boldsymbol{\mathrm{ctg}}^{\mathrm{2}} \left(\frac{\pi}{\mathrm{9}}\right)=?\:\:\:\:\:\:\:\:\: \\ $$$$ \\ $$$$ \\ $$$$ \\ $$$$ \\ $$

Question Number 204337 Answers: 1 Comments: 0

Question Number 204334 Answers: 2 Comments: 0

Question Number 204330 Answers: 1 Comments: 0

Question Number 204329 Answers: 2 Comments: 0

solve (1/([x]))+(1/([2x]))={x}+(1/3)

$${solve}\:\frac{\mathrm{1}}{\left[{x}\right]}+\frac{\mathrm{1}}{\left[\mathrm{2}{x}\right]}=\left\{{x}\right\}+\frac{\mathrm{1}}{\mathrm{3}} \\ $$

Question Number 204328 Answers: 0 Comments: 1

Question Number 204323 Answers: 0 Comments: 0

Question Number 204321 Answers: 0 Comments: 0

Question Number 204318 Answers: 1 Comments: 0

Question Number 204313 Answers: 1 Comments: 0

lim((3×^2 −8×−16)/(2×^2 9×+4))

$${lim}\frac{\mathrm{3}×^{\mathrm{2}} −\mathrm{8}×−\mathrm{16}}{\mathrm{2}×^{\mathrm{2}} \mathrm{9}×+\mathrm{4}} \\ $$$$ \\ $$

Question Number 204303 Answers: 1 Comments: 0

Question Number 204302 Answers: 1 Comments: 0

Question Number 204300 Answers: 1 Comments: 0

x^2 log_3 x^2 −(2x^2 +3)log_9 (2x+3)=3log_3 ((x/(2x+3)))

$${x}^{\mathrm{2}} \mathrm{log}_{\mathrm{3}} {x}^{\mathrm{2}} −\left(\mathrm{2}{x}^{\mathrm{2}} +\mathrm{3}\right)\mathrm{log}_{\mathrm{9}} \left(\mathrm{2}{x}+\mathrm{3}\right)=\mathrm{3log}_{\mathrm{3}} \left(\frac{{x}}{\mathrm{2}{x}+\mathrm{3}}\right) \\ $$

Question Number 204293 Answers: 1 Comments: 1

Prove the following trig identity: ((2sinα+sin3α+sin5α)/(cosα−2cos2α+cos3α))=((2cos2α)/(tan(α/2)))

$$\mathrm{Prove}\:\mathrm{the}\:\mathrm{following}\:\mathrm{trig}\:\mathrm{identity}: \\ $$$$\frac{\mathrm{2sin}\alpha+\mathrm{sin3}\alpha+\mathrm{sin5}\alpha}{\mathrm{cos}\alpha−\mathrm{2cos2}\alpha+\mathrm{cos3}\alpha}=\frac{\mathrm{2cos2}\alpha}{\mathrm{tan}\frac{\alpha}{\mathrm{2}}} \\ $$

Question Number 204279 Answers: 0 Comments: 1

Question Number 204278 Answers: 1 Comments: 3

cos x+cos 3x+cos 5x=(√2)+1 sin x+sin3x+ sin 5x=1 tan 3x=?

$$\mathrm{cos}\:{x}+\mathrm{cos}\:\mathrm{3}{x}+\mathrm{cos}\:\mathrm{5}{x}=\sqrt{\mathrm{2}}+\mathrm{1} \\ $$$$\mathrm{sin}\:{x}+\mathrm{sin3}{x}+\:\mathrm{sin}\:\mathrm{5}{x}=\mathrm{1} \\ $$$$\mathrm{tan}\:\mathrm{3}{x}=? \\ $$

Question Number 204276 Answers: 0 Comments: 0

Question Number 204275 Answers: 1 Comments: 0

Show that ∫_0 ^(π/4) (√(tan x)) (√(1−tan x)) dx=(((√((√2)−1))/( (√2)))−1)π

$$\mathrm{Show}\:\mathrm{that} \\ $$$$\underset{\mathrm{0}} {\overset{\frac{\pi}{\mathrm{4}}} {\int}}\sqrt{\mathrm{tan}\:{x}}\:\sqrt{\mathrm{1}−\mathrm{tan}\:{x}}\:{dx}=\left(\frac{\sqrt{\sqrt{\mathrm{2}}−\mathrm{1}}}{\:\sqrt{\mathrm{2}}}−\mathrm{1}\right)\pi \\ $$

Question Number 204273 Answers: 1 Comments: 0

f(x)=(1/((x−1)^(ln((2/4))) )) Domain f(x) =?

$$\mathrm{f}\left(\mathrm{x}\right)=\frac{\mathrm{1}}{\left(\mathrm{x}−\mathrm{1}\right)^{\mathrm{ln}\left(\frac{\mathrm{2}}{\mathrm{4}}\right)} } \\ $$$$\mathrm{Domain}\:\mathrm{f}\left(\mathrm{x}\right)\:=? \\ $$

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