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Question Number 108710 Answers: 0 Comments: 1

calculate ∫_(−∞) ^∞ (((−1)^x^2 )/((x^2 +x+1)^2 ))dx

$$\mathrm{calculate}\:\:\int_{−\infty} ^{\infty} \:\:\frac{\left(−\mathrm{1}\right)^{\mathrm{x}^{\mathrm{2}} } }{\left(\mathrm{x}^{\mathrm{2}} +\mathrm{x}+\mathrm{1}\right)^{\mathrm{2}} }\mathrm{dx} \\ $$

Question Number 108706 Answers: 0 Comments: 0

calculate lim_(n→+∞) (n^2 −n+1)^(1/(ln(n^2 +3n+2)))

$$\mathrm{calculate}\:\mathrm{lim}_{\mathrm{n}\rightarrow+\infty} \left(\mathrm{n}^{\mathrm{2}} −\mathrm{n}+\mathrm{1}\right)^{\frac{\mathrm{1}}{\mathrm{ln}\left(\mathrm{n}^{\mathrm{2}} +\mathrm{3n}+\mathrm{2}\right)}} \\ $$

Question Number 108705 Answers: 1 Comments: 0

if Σ_(k=1) ^n u_k =n(2^n +3) determine lim_(n→+∞) Σ_(k=1) ^n (1/u_k )

$$\mathrm{if}\:\sum_{\mathrm{k}=\mathrm{1}} ^{\mathrm{n}} \:\mathrm{u}_{\mathrm{k}} =\mathrm{n}\left(\mathrm{2}^{\mathrm{n}} +\mathrm{3}\right)\:\:\mathrm{determine}\:\mathrm{lim}_{\mathrm{n}\rightarrow+\infty} \sum_{\mathrm{k}=\mathrm{1}} ^{\mathrm{n}} \:\frac{\mathrm{1}}{\mathrm{u}_{\mathrm{k}} } \\ $$

Question Number 108699 Answers: 0 Comments: 0

Question Number 108698 Answers: 0 Comments: 0

Question Number 108697 Answers: 1 Comments: 0

Question Number 108692 Answers: 2 Comments: 0

Question Number 108690 Answers: 0 Comments: 0

Question Number 108688 Answers: 0 Comments: 4

prove that Σ_(n=−∞) ^∞ (1/((ax+1)^n )) =−(π/a^n ) lim_(x→−(1/a)) (1/((n−1)!)){cotan(πx)}^((n−1))

$${prove}\:{that}\: \\ $$$$\sum_{{n}=−\infty} ^{\infty} \:\frac{\mathrm{1}}{\left({ax}+\mathrm{1}\right)^{{n}} } \\ $$$$=−\frac{\pi}{{a}^{{n}} }\:{lim}_{{x}\rightarrow−\frac{\mathrm{1}}{{a}}} \:\:\:\frac{\mathrm{1}}{\left({n}−\mathrm{1}\right)!}\left\{{cotan}\left(\pi{x}\right)\right\}^{\left({n}−\mathrm{1}\right)} \\ $$

Question Number 108680 Answers: 0 Comments: 1

Question Number 108679 Answers: 1 Comments: 0

Question Number 108678 Answers: 2 Comments: 0

Question Number 108674 Answers: 2 Comments: 0

Solve log_3 (y−2)+log_y (y+5)=2

$$\mathrm{Solve}\:\:\mathrm{log}_{\mathrm{3}} \left(\mathrm{y}−\mathrm{2}\right)+\mathrm{log}_{\mathrm{y}} \left(\mathrm{y}+\mathrm{5}\right)=\mathrm{2} \\ $$

Question Number 108667 Answers: 4 Comments: 0

Question Number 108664 Answers: 1 Comments: 0

∫_0 ^( 2) ∫_0 ^( 2) x^2 sin(xy)dxdy

$$\int_{\mathrm{0}} ^{\:\mathrm{2}} \int_{\mathrm{0}} ^{\:\mathrm{2}} {x}^{\mathrm{2}} {sin}\left({xy}\right){dxdy} \\ $$

Question Number 108663 Answers: 1 Comments: 0

Question Number 108652 Answers: 1 Comments: 1

Question Number 108845 Answers: 0 Comments: 0

Question Number 108644 Answers: 4 Comments: 1

((bemath)/★) find the value of sin ((π/9))sin (((2π)/9))sin (((3π)/9))sin (((4π)/9))?

$$\:\:\:\frac{{bemath}}{\bigstar} \\ $$$${find}\:{the}\:{value}\:{of}\: \\ $$$$\mathrm{sin}\:\left(\frac{\pi}{\mathrm{9}}\right)\mathrm{sin}\:\left(\frac{\mathrm{2}\pi}{\mathrm{9}}\right)\mathrm{sin}\:\left(\frac{\mathrm{3}\pi}{\mathrm{9}}\right)\mathrm{sin}\:\left(\frac{\mathrm{4}\pi}{\mathrm{9}}\right)?\: \\ $$

Question Number 108643 Answers: 2 Comments: 0

Question Number 108638 Answers: 1 Comments: 0

((bemath)/★) prove that (((n−1)),(( r)) ) + (((n−1)),((r−1)) ) = ((n),(r) )

$$\:\:\:\frac{{bemath}}{\bigstar} \\ $$$${prove}\:{that}\:\begin{pmatrix}{{n}−\mathrm{1}}\\{\:\:\:\:\:{r}}\end{pmatrix}\:+\:\begin{pmatrix}{{n}−\mathrm{1}}\\{{r}−\mathrm{1}}\end{pmatrix}\:=\:\begin{pmatrix}{{n}}\\{{r}}\end{pmatrix} \\ $$

Question Number 108637 Answers: 2 Comments: 0

Question Number 108628 Answers: 0 Comments: 4

Prove that the inequality ∣cos x∣ ≥ 1 − sin^2 x hold true for all x ∈ R

$$\mathrm{Prove}\:\mathrm{that}\:\mathrm{the}\:\mathrm{inequality}\:\:\mid\mathrm{cos}\:\mathrm{x}\mid\:\:\geqslant\:\:\:\mathrm{1}\:\:−\:\:\mathrm{sin}^{\mathrm{2}} \mathrm{x}\:\:\:\:\mathrm{hold}\:\mathrm{true}\:\mathrm{for}\:\mathrm{all}\:\:\mathrm{x}\:\in\:\mathbb{R} \\ $$

Question Number 108626 Answers: 1 Comments: 0

Question Number 108623 Answers: 3 Comments: 0

((⊃BeMath⊃)/★) (1)lim_(b→a) ((b(√a)−a(√b))/(a(√a)+b(√a)−2a(√a))) (2) lim_(x→0) ((3e^(2x) +e^x −4)/x)

$$\:\:\frac{\supset\mathcal{B}{e}\mathcal{M}{ath}\supset}{\bigstar} \\ $$$$\:\left(\mathrm{1}\right)\underset{{b}\rightarrow{a}} {\mathrm{lim}}\:\frac{{b}\sqrt{{a}}−{a}\sqrt{{b}}}{{a}\sqrt{{a}}+{b}\sqrt{{a}}−\mathrm{2}{a}\sqrt{{a}}} \\ $$$$\left(\mathrm{2}\right)\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{3}{e}^{\mathrm{2}{x}} +{e}^{{x}} −\mathrm{4}}{{x}} \\ $$

Question Number 108619 Answers: 1 Comments: 3

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