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AllQuestion and Answers: Page 1125

Question Number 105189 Answers: 0 Comments: 2

Question Number 105181 Answers: 1 Comments: 0

graph the function x^2 +(y−(x^2 )^(1/3) )^2 =1

$${graph}\:{the}\:{function}\:{x}^{\mathrm{2}} +\left({y}−\sqrt[{\mathrm{3}}]{{x}^{\mathrm{2}} }\right)^{\mathrm{2}} =\mathrm{1} \\ $$

Question Number 105235 Answers: 1 Comments: 0

(x−2)^(log _2 (x^2 −5x+5)) > (x−2)^(log _2 (x−3))

$$\left({x}−\mathrm{2}\right)^{\mathrm{log}\:_{\mathrm{2}} \left({x}^{\mathrm{2}} −\mathrm{5}{x}+\mathrm{5}\right)} \:>\:\left({x}−\mathrm{2}\right)^{\mathrm{log}\:_{\mathrm{2}} \left({x}−\mathrm{3}\right)} \\ $$

Question Number 142176 Answers: 1 Comments: 0

∫ e^(ax) sin bx dx = ?

$$\int\:{e}^{{ax}} \:{sin}\:{bx}\:{dx}\:=\:? \\ $$

Question Number 105167 Answers: 1 Comments: 1

Question Number 105163 Answers: 2 Comments: 0

x^2 y′′+xy′−y=(1/(1+x^2 ))

$${x}^{\mathrm{2}} {y}''+{xy}'−{y}=\frac{\mathrm{1}}{\mathrm{1}+{x}^{\mathrm{2}} } \\ $$

Question Number 105158 Answers: 4 Comments: 0

{ ((xy+x+y = 20)),((x^2 +y^2 = 40)) :}find x and y

$$\begin{cases}{{xy}+{x}+{y}\:=\:\mathrm{20}}\\{{x}^{\mathrm{2}} +{y}^{\mathrm{2}} \:=\:\mathrm{40}}\end{cases}{find}\:{x}\:{and}\:{y} \\ $$

Question Number 105157 Answers: 1 Comments: 0

lim_(x→(π/6)) ((cos^2 (((3x)/2))−sin x)/(sin x+(√3) cos x−2)) ?

$$\underset{{x}\rightarrow\frac{\pi}{\mathrm{6}}} {\mathrm{lim}}\:\frac{\mathrm{cos}\:^{\mathrm{2}} \left(\frac{\mathrm{3}{x}}{\mathrm{2}}\right)−\mathrm{sin}\:{x}}{\mathrm{sin}\:{x}+\sqrt{\mathrm{3}}\:\mathrm{cos}\:{x}−\mathrm{2}}\:? \\ $$

Question Number 105155 Answers: 1 Comments: 0

Question Number 105132 Answers: 12 Comments: 0

Question Number 105130 Answers: 0 Comments: 0

To now the real sequence in the follwing image : a_1 =1 ,a_2 =2 a_(nk +1) = ((a_(2k−1) +a_(2k) )/2) ∀ k ∈ Z^+ a_(2k+2) = (√(a_(2k) a_(2k+1) )) then prove that : lim_(n→∞) a_n = ((3(√3))/π)

$${To}\:{now}\:{the}\:{real}\:{sequence}\:{in}\:{the} \\ $$$${follwing}\:{image}\:: \\ $$$${a}_{\mathrm{1}} =\mathrm{1}\:\:\:,{a}_{\mathrm{2}} =\mathrm{2} \\ $$$${a}_{{nk}\:+\mathrm{1}} \:=\:\frac{{a}_{\mathrm{2}{k}−\mathrm{1}} \:+{a}_{\mathrm{2}{k}} }{\mathrm{2}}\:\:\:\:\:\:\:\:\:\:\:\forall\:{k}\:\in\:{Z}^{+} \\ $$$${a}_{\mathrm{2}{k}+\mathrm{2}} \:=\:\sqrt{{a}_{\mathrm{2}{k}} \:{a}_{\mathrm{2}{k}+\mathrm{1}} } \\ $$$${then}\: \\ $$$${prove}\:{that}\::\:\underset{{n}\rightarrow\infty} {\mathrm{lim}}\:{a}_{{n}} \:=\:\frac{\mathrm{3}\sqrt{\mathrm{3}}}{\pi} \\ $$$$ \\ $$

Question Number 105126 Answers: 2 Comments: 0

lim_(x→(π/4)) ((sin x+cos x−(√2)tan x)/(sin x−cos x))

$$\underset{{x}\rightarrow\frac{\pi}{\mathrm{4}}} {\mathrm{lim}}\:\frac{\mathrm{sin}\:{x}+\mathrm{cos}\:{x}−\sqrt{\mathrm{2}}\mathrm{tan}\:{x}}{\mathrm{sin}\:{x}−\mathrm{cos}\:{x}} \\ $$

Question Number 142171 Answers: 3 Comments: 0

lim_(x→0) ((x(1−cos x)^2 )/(sin^3 x−tan^3 x)) =?

$$\:\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{{x}\left(\mathrm{1}−\mathrm{cos}\:{x}\right)^{\mathrm{2}} }{\mathrm{sin}\:^{\mathrm{3}} {x}−\mathrm{tan}\:^{\mathrm{3}} {x}}\:=? \\ $$

Question Number 142168 Answers: 0 Comments: 1

Question Number 142167 Answers: 1 Comments: 0

Find max & min of function f(x)=4tan x+3cot x

$$\:\:\:{Find}\:{max}\:\&\:{min}\:{of}\:{function} \\ $$$$\:\:{f}\left({x}\right)=\mathrm{4tan}\:{x}+\mathrm{3cot}\:{x} \\ $$

Question Number 105124 Answers: 1 Comments: 0

x^4 +ax^3 +bx^2 +cx+d=0 Find x.

$${x}^{\mathrm{4}} +{ax}^{\mathrm{3}} +{bx}^{\mathrm{2}} +{cx}+{d}=\mathrm{0} \\ $$$${Find}\:{x}. \\ $$

Question Number 105118 Answers: 1 Comments: 0

x^2 y′′+xy′−y = (1/(x+1))

$${x}^{\mathrm{2}} {y}''+{xy}'−{y}\:=\:\frac{\mathrm{1}}{{x}+\mathrm{1}}\: \\ $$

Question Number 105114 Answers: 2 Comments: 0

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

$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\mathrm{2}−\sqrt[{\mathrm{3}}]{\mathrm{1}−\mathrm{sin}\:\:^{\mathrm{2}} \left(\mathrm{3}{x}\right)}−\sqrt[{\mathrm{3}}]{\mathrm{1}−\mathrm{sin}\:\:^{\mathrm{2}} \left(\mathrm{2}{x}\right)}}{{x}^{\mathrm{2}} } \\ $$

Question Number 105113 Answers: 2 Comments: 0

Question Number 105112 Answers: 2 Comments: 0

2(√3) sin^2 (x+((3π)/2)) + sin 2x = 0 0≤x≤2π

$$\mathrm{2}\sqrt{\mathrm{3}}\:\mathrm{sin}\:^{\mathrm{2}} \left({x}+\frac{\mathrm{3}\pi}{\mathrm{2}}\right)\:+\:\mathrm{sin}\:\mathrm{2}{x}\:=\:\mathrm{0}\: \\ $$$$\mathrm{0}\leqslant{x}\leqslant\mathrm{2}\pi\: \\ $$

Question Number 105106 Answers: 3 Comments: 0

lim_(x→0) ((sin (πcos^2 x))/(3x^2 )) ?

$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\mathrm{sin}\:\left(\pi\mathrm{cos}\:^{\mathrm{2}} {x}\right)}{\mathrm{3}{x}^{\mathrm{2}} }\:? \\ $$

Question Number 105104 Answers: 2 Comments: 0

lim_(x→0) ((1−cos^5 (x)cos^3 (2x)cos^3 (3x))/(22x^2 ))?

$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\mathrm{1}−\mathrm{cos}\:^{\mathrm{5}} \left({x}\right)\mathrm{cos}\:^{\mathrm{3}} \left(\mathrm{2}{x}\right)\mathrm{cos}\:^{\mathrm{3}} \left(\mathrm{3}{x}\right)}{\mathrm{22}{x}^{\mathrm{2}} }? \\ $$

Question Number 105120 Answers: 1 Comments: 0

f(2f(x)+f(y))=2x+y f:R→R f(x)=? x,y∈R

$${f}\left(\mathrm{2}{f}\left({x}\right)+{f}\left({y}\right)\right)=\mathrm{2}{x}+{y}\:\:\:{f}:\mathbb{R}\rightarrow\mathbb{R} \\ $$$${f}\left({x}\right)=?\:\:\:\:{x},{y}\in\mathbb{R} \\ $$$$ \\ $$

Question Number 105083 Answers: 0 Comments: 0

Question Number 105082 Answers: 0 Comments: 0

Question Number 105080 Answers: 2 Comments: 0

solve: x((x^2 −1)!) = 5((x−1)!)

$${solve}: \\ $$$$\:{x}\left(\left({x}^{\mathrm{2}} −\mathrm{1}\right)!\right)\:=\:\mathrm{5}\left(\left({x}−\mathrm{1}\right)!\right) \\ $$

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