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Question Number 226850 Answers: 0 Comments: 0

Question Number 226830 Answers: 0 Comments: 0

Question Number 226829 Answers: 0 Comments: 0

Question Number 226828 Answers: 0 Comments: 0

(d^π /dx^π )(x^π )=?

$$\frac{{d}^{\pi} }{{dx}^{\pi} }\left({x}^{\pi} \right)=? \\ $$

Question Number 226821 Answers: 1 Comments: 0

Differentiate 20sin (x+3)cos (x^2 /2)

$${Differentiate}\:\: \\ $$$$\mathrm{20sin}\:\left({x}+\mathrm{3}\right)\mathrm{cos}\:\frac{{x}^{\mathrm{2}} }{\mathrm{2}} \\ $$

Question Number 226820 Answers: 1 Comments: 0

Differentiate x^x^x

$$ \\ $$$$\:\:\:\:\:{Differentiate}\:\:\:\:{x}^{{x}^{{x}} } \\ $$$$ \\ $$

Question Number 226819 Answers: 1 Comments: 0

Evaluate ∫_0 ^∞ (dx/(1+x^2 ))

$${Evaluate} \\ $$$$\int_{\mathrm{0}} ^{\infty} \frac{{dx}}{\mathrm{1}+{x}^{\mathrm{2}} } \\ $$

Question Number 226818 Answers: 1 Comments: 0

Evaluate ∫((x^2 +2x−1)/(2x^3 +3x^2 −2x))dx

$${Evaluate} \\ $$$$\int\frac{{x}^{\mathrm{2}} +\mathrm{2}{x}−\mathrm{1}}{\mathrm{2}{x}^{\mathrm{3}} +\mathrm{3}{x}^{\mathrm{2}} −\mathrm{2}{x}}{dx} \\ $$

Question Number 226815 Answers: 1 Comments: 0

lim_(x→0) (lim_(n→∞) (cos (x/2) cos (x/2^2 ) ... cos (x/2^n ))) = ?

$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\left(\underset{{n}\rightarrow\infty} {\mathrm{lim}}\left(\mathrm{cos}\:\frac{{x}}{\mathrm{2}}\:\mathrm{cos}\:\frac{{x}}{\mathrm{2}^{\mathrm{2}} }\:...\:\mathrm{cos}\:\frac{{x}}{\mathrm{2}^{{n}} }\right)\right)\:=\:? \\ $$

Question Number 226812 Answers: 1 Comments: 1

if 28x+30y+31z=360 with x, y, z being positive integers, find x+y+z=?

$${if}\:\mathrm{28}{x}+\mathrm{30}{y}+\mathrm{31}{z}=\mathrm{360}\:{with}\:{x},\:{y},\:{z} \\ $$$${being}\:{positive}\:{integers},\:{find} \\ $$$${x}+{y}+{z}=? \\ $$

Question Number 226809 Answers: 0 Comments: 0

φ_E =∮_S (q/(4πε)) dω

$$\phi_{{E}} =\oint_{{S}} \frac{{q}}{\mathrm{4}\pi\epsilon}\:{d}\omega \\ $$

Question Number 226799 Answers: 2 Comments: 0

∫_0 ^1 ((ln(1+x^2 ))/(1+x)) dx = ?

$$\int_{\mathrm{0}} ^{\mathrm{1}} \frac{\mathrm{ln}\left(\mathrm{1}+{x}^{\mathrm{2}} \right)}{\mathrm{1}+{x}}\:\mathrm{d}{x}\:=\:? \\ $$

Question Number 226798 Answers: 1 Comments: 0

let gcd(m,n)=1. Determine gcd(5^m +7^m ,5^n +7^n )

$${let}\:{gcd}\left({m},{n}\right)=\mathrm{1}.\:{Determine}\:{gcd}\left(\mathrm{5}^{{m}} +\mathrm{7}^{{m}} ,\mathrm{5}^{{n}} +\mathrm{7}^{{n}} \right) \\ $$

Question Number 226796 Answers: 1 Comments: 0

Question Number 226785 Answers: 0 Comments: 13

Question Number 226780 Answers: 1 Comments: 0

By using concept of complex number show that tan 5θ=((tan^5 θ−10tan^3 θ+5tan θ)/(5tan^4 θ−10tan^2 θ+1))

$${By}\:{using}\:{concept}\:{of}\:{complex} \\ $$$${number} \\ $$$${show}\:{that} \\ $$$$\mathrm{tan}\:\mathrm{5}\theta=\frac{\mathrm{tan}\:^{\mathrm{5}} \theta−\mathrm{10tan}\:^{\mathrm{3}} \theta+\mathrm{5tan}\:\theta}{\mathrm{5tan}\:^{\mathrm{4}} \theta−\mathrm{10tan}\:^{\mathrm{2}} \theta+\mathrm{1}} \\ $$

Question Number 226779 Answers: 1 Comments: 0

By using De Moivres theorm simplify (a)(((cos (π/2)−isin (π/2))(cos (π/3)+isin (π/3)))/(cos (π/3)−isin (π/3))) (b)((cos (π/8)+isin (π/8))/(cos (π/6)+isin (π/6)))

Question Number 226778 Answers: 0 Comments: 0

Solve the following D.E (a) (dy/dx)+2y=xy^2 (b) (dy/dx)+3(y/x)=2x^4 y^4

$${Solve}\:{the}\:{following}\:{D}.{E} \\ $$$$\left({a}\right)\:\frac{{dy}}{{dx}}+\mathrm{2}{y}={xy}^{\mathrm{2}} \\ $$$$\left({b}\right)\:\frac{{dy}}{{dx}}+\mathrm{3}\frac{{y}}{{x}}=\mathrm{2}{x}^{\mathrm{4}} {y}^{\mathrm{4}} \\ $$

Question Number 226777 Answers: 4 Comments: 0

Show that ∫_0 ^1 x^2 (1+x^2 )^(−1) dx=((4−π)/4) Hence by using Simpson^′ s rule find the value of π with eleven ordinates. correct to 4 decimal places

$${Show}\:{that} \\ $$$$\:\int_{\mathrm{0}} ^{\mathrm{1}} {x}^{\mathrm{2}} \left(\mathrm{1}+{x}^{\mathrm{2}} \right)^{−\mathrm{1}} {dx}=\frac{\mathrm{4}−\pi}{\mathrm{4}} \\ $$$${Hence}\:{by}\:{using}\:{Simpson}^{'} {s} \\ $$$${rule}\:{find}\:{the}\:{value}\:\:{of}\:\pi\:{with}\: \\ $$$${eleven}\:{ordinates}. \\ $$$${correct}\:{to}\:\mathrm{4}\:{decimal}\:{places} \\ $$

Question Number 226776 Answers: 4 Comments: 0

Approximate ∫_0 ^1 xe^x^2 dx with 6 ordinates. Use both rules Simpsons and Trapozoidal rules,hence evaluate and calculate the percentage error commetted for each case.Give comments

$${Approximate}\:\int_{\mathrm{0}} ^{\mathrm{1}} {xe}^{{x}^{\mathrm{2}} } {dx}\:{with}\:\mathrm{6}\:{ordinates}. \\ $$$${Use}\:{both}\:{rules}\:{Simpsons}\:{and} \\ $$$${Trapozoidal}\:{rules},{hence}\:{evaluate}\:{and} \\ $$$${calculate}\:{the}\:{percentage}\:{error} \\ $$$${commetted}\:{for}\:{each}\:{case}.{Give}\:{comments} \\ $$$$ \\ $$

Question Number 226775 Answers: 0 Comments: 0

Prove that (a−b)(a−c)(a−d)(b−c)(b−d)(c−d) divisible by 12

$${Prove}\:{that}\:\left({a}−{b}\right)\left({a}−{c}\right)\left({a}−{d}\right)\left({b}−{c}\right)\left({b}−{d}\right)\left({c}−{d}\right)\:{divisible}\:{by}\:\mathrm{12} \\ $$

Question Number 226771 Answers: 2 Comments: 0

Question Number 226770 Answers: 2 Comments: 0

Question Number 226766 Answers: 1 Comments: 0

Question Number 226755 Answers: 2 Comments: 0

Question Number 226745 Answers: 1 Comments: 2

if (x/(lm−n^2 ))=(y/(mn−l^2 ))=(z/(nl−m^2 )) then show lx+my+nz=0

$${if}\:\frac{{x}}{{lm}−{n}^{\mathrm{2}} }=\frac{{y}}{{mn}−{l}^{\mathrm{2}} }=\frac{{z}}{{nl}−{m}^{\mathrm{2}} } \\ $$$${then}\:{show}\:{lx}+{my}+{nz}=\mathrm{0} \\ $$$$ \\ $$

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