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Question Number 199570 Answers: 1 Comments: 0

I = ∫_0 ^(π/2) tan^(−1) (((sinx )/2))dx

$$\:\:\:\:\:\:\:\:\mathrm{I}\:\:\:\:\:=\:\:\:\:\int_{\mathrm{0}} ^{\pi/\mathrm{2}} \mathrm{tan}^{−\mathrm{1}} \left(\frac{\mathrm{sin}{x}\:}{\mathrm{2}}\right){dx} \\ $$

Question Number 199568 Answers: 1 Comments: 1

Question Number 199553 Answers: 1 Comments: 0

lim_(x→0) ((tan ((x/2))−sin ((x/2)))/(x^2 ((√(x^2 +x−2))−(√(x^2 +2x−2)) ))) =?

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

Question Number 199550 Answers: 2 Comments: 0

If x = (√(7 + 4(√3))) Find: ((x^4 − x^3 − 9x^2 − 2x + 5)/(x^2 − 4x + 3)) = ?

$$\mathrm{If} \\ $$$$\mathrm{x}\:=\:\sqrt{\mathrm{7}\:+\:\mathrm{4}\sqrt{\mathrm{3}}} \\ $$$$\mathrm{Find}: \\ $$$$\frac{\mathrm{x}^{\mathrm{4}} \:−\:\mathrm{x}^{\mathrm{3}} \:−\:\mathrm{9x}^{\mathrm{2}} \:−\:\mathrm{2x}\:+\:\mathrm{5}}{\mathrm{x}^{\mathrm{2}} \:−\:\mathrm{4x}\:+\:\mathrm{3}}\:\:=\:\:? \\ $$

Question Number 199547 Answers: 3 Comments: 0

Question Number 199544 Answers: 1 Comments: 2

((Area(ydllow))/(Area(Blue)))=?

$$\:\:\frac{\boldsymbol{\mathrm{Area}}\left(\boldsymbol{{ydllow}}\right)}{\boldsymbol{\mathrm{Area}}\left(\boldsymbol{{Blue}}\right)}=? \\ $$

Question Number 199587 Answers: 0 Comments: 1

I konw that Bosons are with even number of proton and neutron and eletron but I am not sure of that fermions. Can someone help answer the question below? Which of this belongs to bosons or fermions? 1. 12C (Carbon−12) 2. 12C^+ ion 3. 4He^+ 4. H^− 5. 13C 6. Positron atom

$$ \\ $$$${I}\:{konw}\:{that}\:{Bosons}\:{are}\:{with}\:{even}\:{number}\:{of}\: \\ $$$${proton}\:{and}\:{neutron}\:{and}\:{eletron}\:{but}\:{I}\:{am}\:{not}\:{sure} \\ $$$${of}\:{that}\:{fermions}.\: \\ $$$${Can}\:{someone}\:{help}\:{answer}\:{the}\:{question}\:{below}? \\ $$$$ \\ $$$${Which}\:{of}\:{this}\:{belongs}\:{to}\:{bosons}\:{or}\:{fermions}? \\ $$$$\mathrm{1}.\:\mathrm{12}{C}\:\left({Carbon}−\mathrm{12}\right) \\ $$$$\mathrm{2}.\:\mathrm{12}{C}^{+} \:{ion} \\ $$$$\mathrm{3}.\:\mathrm{4}{He}^{+} \\ $$$$\mathrm{4}.\:{H}^{−} \\ $$$$\mathrm{5}.\:\mathrm{13}{C} \\ $$$$\mathrm{6}.\:{Positron}\:{atom} \\ $$

Question Number 199538 Answers: 1 Comments: 0

Question Number 199531 Answers: 1 Comments: 0

∫_o ^(+oo) ln(atan(x)dx

$$\int_{{o}} ^{+{oo}} {ln}\left({atan}\left({x}\right){dx}\:\right. \\ $$

Question Number 199528 Answers: 0 Comments: 0

Question Number 199522 Answers: 1 Comments: 0

Question Number 199520 Answers: 1 Comments: 0

n^4 +an^3 +bn^2 +cn+d=k^2 (k∈N) a,b,c,d=¿

$${n}^{\mathrm{4}} +{an}^{\mathrm{3}} +{bn}^{\mathrm{2}} +{cn}+{d}={k}^{\mathrm{2}} \:\left({k}\in{N}\right) \\ $$$${a},{b},{c},{d}=¿ \\ $$

Question Number 199511 Answers: 1 Comments: 1

∫_1 ^(+oo) ln(1+lnx)^(−lnx) dx

$$\int_{\mathrm{1}} ^{+{oo}} {ln}\left(\mathrm{1}+{lnx}\right)^{−{lnx}} \:{dx} \\ $$

Question Number 199510 Answers: 3 Comments: 0

Question Number 199509 Answers: 2 Comments: 2

Question Number 199498 Answers: 2 Comments: 1

Question Number 199486 Answers: 2 Comments: 0

Solve: 100^x = 200

$$\mathrm{Solve}:\:\:\:\mathrm{100}^{\boldsymbol{\mathrm{x}}} \:=\:\mathrm{200} \\ $$

Question Number 199482 Answers: 0 Comments: 3

can someone factor this (3x^3 y−7x^2 +5xy^3 −y^2 )

$$\mathrm{can}\:\mathrm{someone}\:\mathrm{factor}\:\mathrm{this}\:\left(\mathrm{3x}^{\mathrm{3}} \mathrm{y}−\mathrm{7x}^{\mathrm{2}} +\mathrm{5xy}^{\mathrm{3}} −\mathrm{y}^{\mathrm{2}} \right) \\ $$

Question Number 199480 Answers: 0 Comments: 1

Question Number 199471 Answers: 1 Comments: 0

Find the integral ∫_(−3) ^3 { ((x^3 −x),((x≤0))),(x^2 ,((x≥0))) :}dx

$${Find}\:{the}\:{integral} \\ $$$$\int_{−\mathrm{3}} ^{\mathrm{3}} \begin{cases}{{x}^{\mathrm{3}} −{x}}&{\left({x}\leq\mathrm{0}\right)}\\{{x}^{\mathrm{2}} }&{\left({x}\geq\mathrm{0}\right)}\end{cases}{dx} \\ $$

Question Number 199468 Answers: 1 Comments: 0

Question Number 199467 Answers: 1 Comments: 0

Question Number 199466 Answers: 1 Comments: 0

Question Number 199459 Answers: 2 Comments: 0

What minimum value f(x,y)=x^2 +y^2 −z^2 when x+2y+4z=21

$$\:\:\mathrm{What}\:\mathrm{minimum}\:\mathrm{value}\: \\ $$$$\:\:\mathrm{f}\left(\mathrm{x},\mathrm{y}\right)=\mathrm{x}^{\mathrm{2}} +\mathrm{y}^{\mathrm{2}} −\mathrm{z}^{\mathrm{2}} \:\mathrm{when}\: \\ $$$$\:\:\mathrm{x}+\mathrm{2y}+\mathrm{4z}=\mathrm{21} \\ $$

Question Number 199458 Answers: 1 Comments: 0

Solve: log_3 p + log_r 8 =5 r+p=11. find r&p

$$\boldsymbol{{Solve}}:\:\boldsymbol{{log}}_{\mathrm{3}} \boldsymbol{{p}}\:+\:\boldsymbol{{log}}_{\boldsymbol{{r}}} \mathrm{8}\:=\mathrm{5} \\ $$$$\boldsymbol{{r}}+\boldsymbol{{p}}=\mathrm{11}.\:\:\boldsymbol{{find}}\:\boldsymbol{{r\&p}} \\ $$

Question Number 199451 Answers: 3 Comments: 0

Find: 1. lim_(n→∞) (((5n − 25)/(3n + 15)))^(1/(5n)) 2. lim_(x→∞) (((x^3 + 3x^2 + 1))^(1/3) − ((x^3 − 3x^2 + 1))^(1/3) ) 3. lim_(x→0) ((cos 4x^3 − 1)/(sin^6 2x))

$$\mathrm{Find}: \\ $$$$\mathrm{1}.\:\underset{\boldsymbol{\mathrm{n}}\rightarrow\infty} {\mathrm{lim}}\:\sqrt[{\mathrm{5}\boldsymbol{\mathrm{n}}}]{\frac{\mathrm{5n}\:−\:\mathrm{25}}{\mathrm{3n}\:+\:\mathrm{15}}} \\ $$$$\mathrm{2}.\:\underset{\boldsymbol{\mathrm{x}}\rightarrow\infty} {\mathrm{lim}}\:\left(\sqrt[{\mathrm{3}}]{\mathrm{x}^{\mathrm{3}} \:+\:\mathrm{3x}^{\mathrm{2}} \:+\:\mathrm{1}}\:−\:\sqrt[{\mathrm{3}}]{\mathrm{x}^{\mathrm{3}} \:−\:\mathrm{3x}^{\mathrm{2}} \:+\:\mathrm{1}}\:\right) \\ $$$$\mathrm{3}.\:\underset{\boldsymbol{\mathrm{x}}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{cos}\:\mathrm{4x}^{\mathrm{3}} \:−\:\mathrm{1}}{\mathrm{sin}^{\mathrm{6}} \:\mathrm{2x}} \\ $$

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