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Question Number 167662 Answers: 1 Comments: 0

lim_(x→3) [((log((2log(√(x^3 +2))))^(1/3) ))^(1/4) ]=?

$$\underset{{x}\rightarrow\mathrm{3}} {\mathrm{lim}}\left[\sqrt[{\mathrm{4}}]{{log}\sqrt[{\mathrm{3}}]{\mathrm{2}{log}\sqrt{{x}^{\mathrm{3}} +\mathrm{2}}}}\right]=? \\ $$

Question Number 167666 Answers: 1 Comments: 1

I_n =∫(dx/(cos^n x)) Prove that I_n =((n−2)/(n−1))I_(n−2) +((sin x)/((n−1)cos^(n−1) x))

$${I}_{{n}} =\int\frac{{dx}}{\mathrm{cos}\:^{{n}} {x}} \\ $$$${Prove}\:{that} \\ $$$${I}_{{n}} =\frac{{n}−\mathrm{2}}{{n}−\mathrm{1}}{I}_{{n}−\mathrm{2}} +\frac{\mathrm{sin}\:{x}}{\left({n}−\mathrm{1}\right)\mathrm{cos}\:^{{n}−\mathrm{1}} {x}} \\ $$

Question Number 167664 Answers: 0 Comments: 0

a=3k,b=4k,c=5k 3k+4k+5k=1000⇒k=500/6 a=1500/6,b=200/6,c=2500/6

$${a}=\mathrm{3}{k},{b}=\mathrm{4}{k},{c}=\mathrm{5}{k} \\ $$$$\mathrm{3}{k}+\mathrm{4}{k}+\mathrm{5}{k}=\mathrm{1000}\Rightarrow{k}=\mathrm{500}/\mathrm{6} \\ $$$${a}=\mathrm{1500}/\mathrm{6},{b}=\mathrm{200}/\mathrm{6},{c}=\mathrm{2500}/\mathrm{6} \\ $$

Question Number 167663 Answers: 1 Comments: 2

lim_(x→2) [log((1/x)+(1/(2x))+(1/(4x)).......)]=?

$$\underset{{x}\rightarrow\mathrm{2}} {\mathrm{lim}}\left[{log}\left(\frac{\mathrm{1}}{{x}}+\frac{\mathrm{1}}{\mathrm{2}{x}}+\frac{\mathrm{1}}{\mathrm{4}{x}}.......\right)\right]=? \\ $$

Question Number 167650 Answers: 1 Comments: 4

{: (( a^2 +b^2 =c^2 )),((a+b+c=1000)) }; a^(?) , b^(?) , c^(?) ∈Z Q#167533 reposted

$$\left.\begin{matrix}{\:\:\:\:\:\:\:\:\:{a}^{\mathrm{2}} +{b}^{\mathrm{2}} ={c}^{\mathrm{2}} }\\{{a}+{b}+{c}=\mathrm{1000}}\end{matrix}\right\};\:\overset{?} {{a}},\:\:\overset{?} {{b}},\:\:\overset{?} {{c}}\in\mathbb{Z} \\ $$$${Q}#\mathrm{167533}\:\mathrm{reposted} \\ $$

Question Number 167648 Answers: 0 Comments: 6

log_(sinx) 2+log_(cosx) 2+log_(sin x) 2×log_(cos x) 2=0 x=?

$$\mathrm{log}_{{sinx}} \mathrm{2}+\mathrm{log}_{{cosx}} \mathrm{2}+{log}_{\mathrm{sin}\:{x}} \mathrm{2}×{log}_{\mathrm{cos}\:{x}} \mathrm{2}=\mathrm{0} \\ $$$${x}=? \\ $$

Question Number 167647 Answers: 2 Comments: 0

Question Number 167626 Answers: 0 Comments: 0

∫_0 ^∞ (e^(−t) /( (√t))) e^(−(1/(4t))) dt

$$\int_{\mathrm{0}} ^{\infty} \frac{{e}^{−{t}} }{\:\sqrt{{t}}}\:{e}^{−\frac{\mathrm{1}}{\mathrm{4}{t}}} \:{dt} \\ $$

Question Number 167624 Answers: 2 Comments: 0

solve Ω =lim_( n→∞) n^( 2) . ln( n . sin((1/n)))=?

$$ \\ $$$$\:\:{solve} \\ $$$$\:\:\Omega\:={lim}_{\:{n}\rightarrow\infty} {n}^{\:\mathrm{2}} .\:{ln}\left(\:{n}\:.\:{sin}\left(\frac{\mathrm{1}}{{n}}\right)\right)=? \\ $$$$ \\ $$

Question Number 167633 Answers: 1 Comments: 6

Question Number 167630 Answers: 0 Comments: 0

Question Number 167617 Answers: 3 Comments: 0

(1)lim_(x→0) [tan((π/4)−x)]^(cotx) =? (2)lim_(x→0) [(1/(sin x))−(1/x)]=?

$$\left(\mathrm{1}\right)\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\left[{tan}\left(\frac{\pi}{\mathrm{4}}−{x}\right)\right]^{{cotx}} =? \\ $$$$\left(\mathrm{2}\right)\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\left[\frac{\mathrm{1}}{\mathrm{sin}\:{x}}−\frac{\mathrm{1}}{{x}}\right]=? \\ $$

Question Number 167616 Answers: 0 Comments: 0

How do i show that A\B⊕C=(A\B)⊕(A\C)

$$\boldsymbol{{How}}\:\boldsymbol{{do}}\:\boldsymbol{{i}}\:\boldsymbol{{show}}\:\boldsymbol{{that}} \\ $$$$\:\boldsymbol{{A}}\backslash\boldsymbol{{B}}\oplus\boldsymbol{{C}}=\left(\boldsymbol{{A}}\backslash\boldsymbol{{B}}\right)\oplus\left(\boldsymbol{{A}}\backslash\boldsymbol{{C}}\right) \\ $$

Question Number 167615 Answers: 0 Comments: 0

lim_(x→1) (((√(3+x)) ((7+x^3 ))^(1/3) −4)/((x−1)^2 )) =?

$$\:\:\:\underset{{x}\rightarrow\mathrm{1}} {\mathrm{lim}}\:\frac{\sqrt{\mathrm{3}+\mathrm{x}}\:\sqrt[{\mathrm{3}}]{\mathrm{7}+\mathrm{x}^{\mathrm{3}} }−\mathrm{4}}{\left(\mathrm{x}−\mathrm{1}\right)^{\mathrm{2}} }\:=? \\ $$$$ \\ $$

Question Number 167612 Answers: 0 Comments: 1

Question Number 167609 Answers: 1 Comments: 0

Question Number 167601 Answers: 0 Comments: 0

Question Number 167598 Answers: 1 Comments: 0

∫ (x/(5x^4 +x^3 −5x−1)) dx=?

$$\:\:\:\:\:\:\int\:\frac{\mathrm{x}}{\mathrm{5x}^{\mathrm{4}} +\mathrm{x}^{\mathrm{3}} −\mathrm{5x}−\mathrm{1}}\:\mathrm{dx}=? \\ $$

Question Number 167596 Answers: 1 Comments: 0

∫ ((cos 7x−cos 8x)/(1+2cos 5x)) dx =?

$$\:\:\int\:\frac{\mathrm{cos}\:\mathrm{7x}−\mathrm{cos}\:\mathrm{8x}}{\mathrm{1}+\mathrm{2cos}\:\mathrm{5x}}\:\mathrm{dx}\:=? \\ $$

Question Number 167594 Answers: 1 Comments: 0

Question Number 167593 Answers: 2 Comments: 0

Question Number 167588 Answers: 1 Comments: 0

1+1=¿

$$\mathrm{1}+\mathrm{1}=¿ \\ $$

Question Number 167586 Answers: 2 Comments: 1

λ=∫ (dx/( (√(1+cos x))+(√(1+sin x)))) =?

$$\:\:\:\:\:\:\:\:\lambda=\int\:\frac{\mathrm{dx}}{\:\sqrt{\mathrm{1}+\mathrm{cos}\:\mathrm{x}}+\sqrt{\mathrm{1}+\mathrm{sin}\:\mathrm{x}}}\:=? \\ $$

Question Number 167628 Answers: 0 Comments: 1

Question Number 167627 Answers: 0 Comments: 0

Question Number 167576 Answers: 1 Comments: 1

prove by useing the polar cordinaite ∫_0 ^( (a/2)) ∫_y ^( (√(a^2 −y^2 ))) x dx dy = ((5 a^3 )/(24 ))

$$\boldsymbol{{prove}}\:\boldsymbol{{by}}\:\boldsymbol{{useing}}\:\boldsymbol{{the}}\:\boldsymbol{{polar}}\:\boldsymbol{{cordinaite}}\: \\ $$$$ \\ $$$$\int_{\mathrm{0}} ^{\:\frac{\boldsymbol{{a}}}{\mathrm{2}}} \:\:\:\int_{\boldsymbol{{y}}} ^{\:\sqrt{\boldsymbol{{a}}^{\mathrm{2}} −\boldsymbol{{y}}^{\mathrm{2}} }} \:\boldsymbol{{x}}\:\boldsymbol{{dx}}\:\boldsymbol{{dy}}\:\:=\:\frac{\mathrm{5}\:\boldsymbol{{a}}^{\mathrm{3}} }{\mathrm{24}\:} \\ $$

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