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Question Number 167838 Answers: 1 Comments: 0

(dy/dx)=8x+4y+(2x+y−1)^2 y=?

$$\:\:\:\:\:\:\frac{{dy}}{{dx}}=\mathrm{8}{x}+\mathrm{4}{y}+\left(\mathrm{2}{x}+{y}−\mathrm{1}\right)^{\mathrm{2}} \\ $$$$\:\:\:\:\:{y}=? \\ $$

Question Number 167830 Answers: 0 Comments: 1

Question Number 167828 Answers: 1 Comments: 0

Houses on one side of a particular street are assigned odd numbers, starting from 11. If the sum of the numbers is 551, how many houses are there?

$$\:\mathrm{Houses}\:\mathrm{on}\:\mathrm{one}\:\mathrm{side}\:\mathrm{of}\:\mathrm{a}\:\mathrm{particular}\: \\ $$$$\:\mathrm{street}\:\mathrm{are}\:\mathrm{assigned}\:\mathrm{odd}\:\mathrm{numbers},\: \\ $$$$\:\mathrm{starting}\:\mathrm{from}\:\mathrm{11}.\:\mathrm{If}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{the}\: \\ $$$$\:\mathrm{numbers}\:\mathrm{is}\:\mathrm{551},\:\mathrm{how}\:\mathrm{many}\:\mathrm{houses} \\ $$$$\:\mathrm{are}\:\mathrm{there}? \\ $$

Question Number 167823 Answers: 1 Comments: 2

Question Number 167821 Answers: 0 Comments: 2

Question Number 167820 Answers: 1 Comments: 0

given x^2 =(π^2 /3)+4Σ(−1)^n ((cos(nx))/n^2 ), show that Σ(1/((2n−1)^2 ))=(π^2 /8)

$$\mathrm{given}\:\:\mathrm{x}^{\mathrm{2}} =\frac{\pi^{\mathrm{2}} }{\mathrm{3}}+\mathrm{4}\Sigma\left(−\mathrm{1}\right)^{\mathrm{n}} \frac{\mathrm{cos}\left(\mathrm{nx}\right)}{\mathrm{n}^{\mathrm{2}} },\:\mathrm{show}\:\mathrm{that}\:\Sigma\frac{\mathrm{1}}{\left(\mathrm{2n}−\mathrm{1}\right)^{\mathrm{2}} }=\frac{\pi^{\mathrm{2}} }{\mathrm{8}} \\ $$

Question Number 167819 Answers: 0 Comments: 0

let f(x)=e^(−x) arctan(2x) find f^((n)) (0)

$${let}\:{f}\left({x}\right)={e}^{−{x}} {arctan}\left(\mathrm{2}{x}\right) \\ $$$${find}\:{f}^{\left({n}\right)} \left(\mathrm{0}\right) \\ $$

Question Number 167800 Answers: 0 Comments: 3

5^(2x) = 2.10^x −4^(2x) (((x−4)^(x^2 +2) ))^(1/((x+2)^(−1) )) =?

$$\:\:\:\:\:\:\mathrm{5}^{\mathrm{2}{x}} \:=\:\mathrm{2}.\mathrm{10}^{{x}} −\mathrm{4}^{\mathrm{2}{x}} \: \\ $$$$\:\:\:\:\:\sqrt[{\left({x}+\mathrm{2}\right)^{−\mathrm{1}} }]{\left({x}−\mathrm{4}\right)^{{x}^{\mathrm{2}} +\mathrm{2}} }=?\: \\ $$

Question Number 167795 Answers: 2 Comments: 1

Question Number 167787 Answers: 2 Comments: 0

Question Number 167785 Answers: 0 Comments: 0

Question Number 167784 Answers: 0 Comments: 0

Question Number 167782 Answers: 1 Comments: 0

etudier l′existance de limite en (0,0) f(x,y)=((x^2 y)/(x+y))

$${etudier}\:{l}'{existance}\:{de}\:{limite}\:{en}\:\left(\mathrm{0},\mathrm{0}\right) \\ $$$${f}\left({x},{y}\right)=\frac{{x}^{\mathrm{2}} {y}}{{x}+{y}} \\ $$

Question Number 167808 Answers: 1 Comments: 1

Question Number 167777 Answers: 1 Comments: 0

Question Number 167776 Answers: 2 Comments: 0

Question Number 167775 Answers: 1 Comments: 1

Question Number 167765 Answers: 0 Comments: 0

show that two permutations are conjugate if their matrices are similar

$$ \\ $$show that two permutations are conjugate if their matrices are similar

Question Number 167773 Answers: 2 Comments: 0

Calculate ∫((xtan x)/(cos^4 x))dx

$${Calculate} \\ $$$$\int\frac{{x}\mathrm{tan}\:{x}}{\mathrm{cos}\:^{\mathrm{4}} {x}}{dx} \\ $$

Question Number 167757 Answers: 1 Comments: 1

Calculate ∫sec^2 xsec xdx

$${Calculate} \\ $$$$\int\mathrm{sec}\:^{\mathrm{2}} {x}\mathrm{sec}\:{xdx} \\ $$

Question Number 167746 Answers: 1 Comments: 1

log_((x^2 +2)) (x^2 +4x)=?

$${log}_{\left({x}^{\mathrm{2}} +\mathrm{2}\right)} \left({x}^{\mathrm{2}} +\mathrm{4}{x}\right)=? \\ $$

Question Number 167740 Answers: 0 Comments: 0

I_n =∫_0 ^(π/4) (1/(cos^(2n+1) x))dx Prove by parts that: 2nI_n =(2n−1)I_(n−1) +(2^n /( (√2)))

$${I}_{{n}} =\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} \frac{\mathrm{1}}{\mathrm{cos}\:^{\mathrm{2}{n}+\mathrm{1}} {x}}{dx} \\ $$$${Prove}\:{by}\:{parts}\:{that}: \\ $$$$\mathrm{2}{nI}_{{n}} =\left(\mathrm{2}{n}−\mathrm{1}\right){I}_{{n}−\mathrm{1}} +\frac{\mathrm{2}^{{n}} }{\:\sqrt{\mathrm{2}}} \\ $$

Question Number 167739 Answers: 4 Comments: 2

Question Number 167738 Answers: 2 Comments: 0

72 → 49 42 → 16 21 → 2 16 → ?

$$\mathrm{72}\:\:\:\rightarrow\:\:\:\mathrm{49} \\ $$$$\mathrm{42}\:\:\:\rightarrow\:\:\:\mathrm{16} \\ $$$$\mathrm{21}\:\:\:\rightarrow\:\:\:\mathrm{2} \\ $$$$\mathrm{16}\:\:\:\rightarrow\:\:\:? \\ $$

Question Number 167737 Answers: 1 Comments: 0

3 □ 4 → 27 4 □ 2 → 36 2 □ 7 → 18 1 □ 9 → ?

$$\mathrm{3}\:\:\:\Box\:\:\:\mathrm{4}\:\:\:\rightarrow\:\:\:\mathrm{27} \\ $$$$\mathrm{4}\:\:\:\Box\:\:\:\mathrm{2}\:\:\:\rightarrow\:\:\:\mathrm{36} \\ $$$$\mathrm{2}\:\:\:\Box\:\:\:\mathrm{7}\:\:\:\rightarrow\:\:\:\mathrm{18} \\ $$$$\mathrm{1}\:\:\:\Box\:\:\:\mathrm{9}\:\:\:\rightarrow\:\:\:? \\ $$

Question Number 167730 Answers: 1 Comments: 2

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