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AllQuestion and Answers: Page 465

Question Number 171475 Answers: 1 Comments: 0

Question Number 171472 Answers: 0 Comments: 0

lim_(a→∞) Σ_(n=1) ^a ((e^(in) .ln∣(1/x)∣)/(πn^2 )).tan^(−1) (n(√π)) Mastermind

$${li}\underset{{a}\rightarrow\infty} {{m}}\:\underset{{n}=\mathrm{1}} {\overset{{a}} {\sum}}\frac{{e}^{{in}} .{ln}\mid\frac{\mathrm{1}}{{x}}\mid}{\pi{n}^{\mathrm{2}} }.{tan}^{−\mathrm{1}} \left({n}\sqrt{\pi}\right) \\ $$$$ \\ $$$${Mastermind} \\ $$

Question Number 171560 Answers: 1 Comments: 1

Nice Integral Ω = ∫_0 ^( (π/4)) (( tan(x))/(( cos^( 2) (x) + 2sin^( 2) (x))))dx =

$$ \\ $$$$\:\:\:\:\:\mathrm{Nice}\:\:\:\mathrm{Integral} \\ $$$$\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\Omega\:=\:\int_{\mathrm{0}} ^{\:\frac{\pi}{\mathrm{4}}} \frac{\:{tan}\left({x}\right)}{\left(\:{cos}^{\:\mathrm{2}} \left({x}\right)\:\:+\:\mathrm{2}{sin}^{\:\mathrm{2}} \left({x}\right)\right)}{dx}\:= \\ $$

Question Number 171484 Answers: 3 Comments: 1

let f(x) = x+(2/(1.3))x^3 +((2.4)/(1.3.5))x^5 +((2.4.6)/(1.3.5.7))x^7 +......... ∀x∈(0,1) the value of f((1/( (√2)))) = ?

$$ \\ $$$$\:\:\:\:{let}\:{f}\left({x}\right)\:=\:{x}+\frac{\mathrm{2}}{\mathrm{1}.\mathrm{3}}{x}^{\mathrm{3}} +\frac{\mathrm{2}.\mathrm{4}}{\mathrm{1}.\mathrm{3}.\mathrm{5}}{x}^{\mathrm{5}} +\frac{\mathrm{2}.\mathrm{4}.\mathrm{6}}{\mathrm{1}.\mathrm{3}.\mathrm{5}.\mathrm{7}}{x}^{\mathrm{7}} +......... \\ $$$$\:\:\:\:\forall{x}\in\left(\mathrm{0},\mathrm{1}\right)\:\:{the}\:{value}\:{of}\:\:{f}\left(\frac{\mathrm{1}}{\:\sqrt{\mathrm{2}}}\right)\:=\:? \\ $$

Question Number 171464 Answers: 0 Comments: 0

Question Number 171456 Answers: 1 Comments: 1

Question Number 171455 Answers: 1 Comments: 1

find the sum of z = sinx + sin2x+sin3x+......+sinnx

$${find}\:{the}\:{sum}\:{of}\:{z}\:=\:{sinx}\:+\:{sin}\mathrm{2}{x}+{sin}\mathrm{3}{x}+......+{sinnx}\: \\ $$

Question Number 174435 Answers: 0 Comments: 0

sec^2 1°+sec^2 2°+sec^2 3°+...+sec^2 89°=?

$$\:\mathrm{sec}\:^{\mathrm{2}} \mathrm{1}°+\mathrm{sec}\:^{\mathrm{2}} \mathrm{2}°+\mathrm{sec}\:^{\mathrm{2}} \mathrm{3}°+...+\mathrm{sec}\:^{\mathrm{2}} \mathrm{89}°=? \\ $$

Question Number 171448 Answers: 0 Comments: 0

∫_0 ^(𝛑/2) x(√(cos(x)))dx evaluate!!!!

$$\int_{\mathrm{0}} ^{\frac{\boldsymbol{\pi}}{\mathrm{2}}} \boldsymbol{\mathrm{x}}\sqrt{\boldsymbol{\mathrm{cos}}\left(\boldsymbol{\mathrm{x}}\right)}\boldsymbol{\mathrm{dx}}\:\:\:\boldsymbol{\mathrm{evaluate}}!!!! \\ $$

Question Number 171443 Answers: 2 Comments: 0

Question Number 171442 Answers: 0 Comments: 1

Question Number 171437 Answers: 2 Comments: 0

make r the subject of the formula y=(((pr)/m) − (p^3 /1))^(−3/2) find r if y=−8 , m=−1, p=3

$$\mathrm{make}\:\boldsymbol{\mathrm{r}}\:\:\:\mathrm{the}\:\mathrm{subject}\:\mathrm{of}\:\mathrm{the}\:\mathrm{formula} \\ $$$$ \\ $$$$\boldsymbol{\mathrm{y}}=\left(\frac{\boldsymbol{\mathrm{pr}}}{\boldsymbol{\mathrm{m}}}\:\:−\:\frac{\boldsymbol{\mathrm{p}}^{\mathrm{3}} }{\mathrm{1}}\right)^{−\mathrm{3}/\mathrm{2}} \\ $$$$ \\ $$$$\mathrm{find}\:\boldsymbol{\mathrm{r}}\:\mathrm{if}\:\mathrm{y}=−\mathrm{8}\:\:\:,\:\:\mathrm{m}=−\mathrm{1},\:\:\mathrm{p}=\mathrm{3} \\ $$

Question Number 171435 Answers: 1 Comments: 7

Let f:R→R be polynomial function satisfying f(x) f((1/x))=f(x)+f((1/x)) and f(3)=28, then f(x) is

$$\:\:{Let}\:{f}:{R}\rightarrow{R}\:{be}\:{polynomial} \\ $$$$\:{function}\:{satisfying}\: \\ $$$$\:{f}\left({x}\right)\:{f}\left(\frac{\mathrm{1}}{{x}}\right)={f}\left({x}\right)+{f}\left(\frac{\mathrm{1}}{{x}}\right)\:{and} \\ $$$$\:{f}\left(\mathrm{3}\right)=\mathrm{28},\:{then}\:{f}\left({x}\right)\:{is} \\ $$

Question Number 171441 Answers: 0 Comments: 1

I_n = −((2n)/(2n + 1)) I_(n−1) I_0 = 1 Show that I_n = (((−4)^n (n!)^2 )/((2n+1)!))

$${I}_{{n}} \:=\:−\frac{\mathrm{2}{n}}{\mathrm{2}{n}\:+\:\mathrm{1}}\:{I}_{{n}−\mathrm{1}} \\ $$$${I}_{\mathrm{0}} \:=\:\mathrm{1} \\ $$$${Show}\:{that}\:{I}_{{n}} \:=\:\frac{\left(−\mathrm{4}\right)^{{n}} \left({n}!\right)^{\mathrm{2}} }{\left(\mathrm{2}{n}+\mathrm{1}\right)!} \\ $$

Question Number 171440 Answers: 0 Comments: 0

Question Number 171431 Answers: 0 Comments: 0

Question Number 171426 Answers: 0 Comments: 0

Question Number 171425 Answers: 0 Comments: 0

Question Number 171423 Answers: 0 Comments: 0

Question Number 171421 Answers: 0 Comments: 0

Prove that arg(e^z )= Im(z) + 2kπ ,k=0,±1,±2,...(√)

$${Prove}\:{that}\:{arg}\left({e}^{{z}} \right)=\:{Im}\left({z}\right)\:+\:\mathrm{2}{k}\pi\:,{k}=\mathrm{0},\pm\mathrm{1},\pm\mathrm{2},...\sqrt{} \\ $$

Question Number 171406 Answers: 1 Comments: 1

1=(√1)=(√((−1)(−1)))=(√((−1)))×(√((−1)))=i.i=i^2 =−1 where is the mistake?

$$\mathrm{1}=\sqrt{\mathrm{1}}=\sqrt{\left(−\mathrm{1}\right)\left(−\mathrm{1}\right)}=\sqrt{\left(−\mathrm{1}\right)}×\sqrt{\left(−\mathrm{1}\right)}=\mathrm{i}.\mathrm{i}=\mathrm{i}^{\mathrm{2}} =−\mathrm{1} \\ $$$$\mathrm{where}\:\mathrm{is}\:\mathrm{the}\:\mathrm{mistake}? \\ $$

Question Number 171403 Answers: 1 Comments: 0

a , b , c ∈R and a≠b≠c and (a/(b+c)) , (b/(a+c)) , (c/(a+b)) are three consecutive terms of AP (Arithmetic progression ) find −: ((b^( 2) −a^( 2) )/(c^( 2) −b^( 2) ))

$$\:\:{a}\:,\:{b}\:,\:{c}\:\in\mathbb{R}\:\:{and}\:\:{a}\neq{b}\neq{c} \\ $$$$\:\:{and}\:\:\:\frac{{a}}{{b}+{c}}\:,\:\frac{{b}}{{a}+{c}}\:,\:\frac{{c}}{{a}+{b}}\:\:\:{are}\:{three}\:{consecutive}\:{terms}\:{of}\:{AP} \\ $$$$\:\:\left({Arithmetic}\:{progression}\:\right) \\ $$$$\:\:{find}\:−:\:\:\:\frac{{b}^{\:\mathrm{2}} −{a}^{\:\mathrm{2}} }{{c}^{\:\mathrm{2}} −{b}^{\:\mathrm{2}} } \\ $$

Question Number 171402 Answers: 2 Comments: 0

solve... ⌊x^( 2) ⌋+⌊x⌋^( 2) = x^( 2) +x +1 x=?

$$\:\:{solve}... \\ $$$$\:\:\:\lfloor{x}^{\:\mathrm{2}} \rfloor+\lfloor{x}\rfloor^{\:\mathrm{2}} =\:{x}^{\:\mathrm{2}} +{x}\:+\mathrm{1} \\ $$$$\:\:\:\:\:\:{x}=? \\ $$

Question Number 171397 Answers: 0 Comments: 3

ax+by+cz=(2/3) x+y+z=18 (1/a)+(1/b)+(1/c)=?

$${ax}+{by}+{cz}=\frac{\mathrm{2}}{\mathrm{3}} \\ $$$${x}+{y}+{z}=\mathrm{18} \\ $$$$\frac{\mathrm{1}}{{a}}+\frac{\mathrm{1}}{{b}}+\frac{\mathrm{1}}{{c}}=? \\ $$

Question Number 171395 Answers: 1 Comments: 2

∫_(−∞) ^(+∞) (x^2 /(1+x^4 ))dx

$$\int_{−\infty} ^{+\infty} \frac{\boldsymbol{{x}}^{\mathrm{2}} }{\mathrm{1}+\boldsymbol{{x}}^{\mathrm{4}} }\boldsymbol{{dx}} \\ $$

Question Number 171392 Answers: 0 Comments: 1

∫_0 ^(π/2) ((cos x)/((1+(√(sin 2x)) )^3 )) dx =?

$$\:\:\underset{\mathrm{0}} {\overset{\frac{\pi}{\mathrm{2}}} {\int}}\:\frac{\mathrm{cos}\:{x}}{\left(\mathrm{1}+\sqrt{\mathrm{sin}\:\mathrm{2}{x}}\:\right)^{\mathrm{3}} }\:{dx}\:=? \\ $$

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