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Question Number 59349 Answers: 0 Comments: 0

Question Number 59347 Answers: 1 Comments: 7

Question Number 59346 Answers: 0 Comments: 0

Question Number 59344 Answers: 2 Comments: 0

∫ e^x (((1−sin x)/(1−cos x)))dx = ?

$$\int\:{e}^{{x}} \left(\frac{\mathrm{1}−\mathrm{sin}\:{x}}{\mathrm{1}−\mathrm{cos}\:{x}}\right){dx}\:=\:? \\ $$

Question Number 59338 Answers: 1 Comments: 1

Question Number 59336 Answers: 1 Comments: 0

Find the nth term of the AP: 2, − (2/5) , − (2/(11)) , ...

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{nth}\:\mathrm{term}\:\mathrm{of}\:\mathrm{the}\:\mathrm{AP}:\:\:\:\:\:\mathrm{2},\:\:\:\:−\:\frac{\mathrm{2}}{\mathrm{5}}\:,\:\:\:\:\:−\:\frac{\mathrm{2}}{\mathrm{11}}\:,\:... \\ $$

Question Number 59335 Answers: 0 Comments: 0

Question Number 59326 Answers: 1 Comments: 1

sin cos^(−1) (−(√(3/2)))

$${sin}\:{cos}^{−\mathrm{1}} \left(−\sqrt{\left.\mathrm{3}/\mathrm{2}\right)}\right. \\ $$

Question Number 59323 Answers: 1 Comments: 0

Question Number 59316 Answers: 2 Comments: 0

Question Number 59313 Answers: 1 Comments: 0

c+6×t c=3 t=5

$$\mathrm{c}+\mathrm{6}×\mathrm{t}\:\:\mathrm{c}=\mathrm{3}\:\:\mathrm{t}=\mathrm{5} \\ $$

Question Number 59305 Answers: 2 Comments: 0

Witthout using mathematical tables or calculator, find,in surdform(radicals) , the value tan22.5°

$$\mathrm{Witthout}\:\mathrm{using}\:\mathrm{mathematical}\:\mathrm{tables}\:\mathrm{or} \\ $$$$\mathrm{calculator},\:\mathrm{find},\mathrm{in}\:\mathrm{surdform}\left(\mathrm{radicals}\right) \\ $$$$,\:\mathrm{the}\:\mathrm{value}\:\mathrm{tan22}.\mathrm{5}° \\ $$

Question Number 59301 Answers: 1 Comments: 4

Question Number 59295 Answers: 1 Comments: 0

Let A be3×3 matrix with eigen values 1,−1,0. Then determinant of I+A^(100 ) =??

$${Let}\:{A}\:{be}\mathrm{3}×\mathrm{3}\:{matrix}\:{with}\:{eigen}\:{values} \\ $$$$\mathrm{1},−\mathrm{1},\mathrm{0}.\:{Then}\:{determinant}\:{of}\:{I}+{A}^{\mathrm{100}\:} =?? \\ $$

Question Number 59287 Answers: 1 Comments: 0

A circle x^2 +y^2 −2x−4y−5=0 with centr 0 is cut by a line y=2x+5 at points P and Q. Show that QO is perpendicular to PO.

$$\mathrm{A}\:\mathrm{circle}\:\mathrm{x}^{\mathrm{2}} +\mathrm{y}^{\mathrm{2}} −\mathrm{2x}−\mathrm{4y}−\mathrm{5}=\mathrm{0}\:\mathrm{with}\:\mathrm{centr} \\ $$$$\mathrm{0}\:\mathrm{is}\:\mathrm{cut}\:\mathrm{by}\:\mathrm{a}\:\mathrm{line}\:\mathrm{y}=\mathrm{2x}+\mathrm{5}\:\mathrm{at}\:\mathrm{points}\:\mathrm{P}\:\mathrm{and}\:\mathrm{Q}. \\ $$$$\mathrm{Show}\:\mathrm{that}\:\mathrm{QO}\:\mathrm{is}\:\mathrm{perpendicular}\:\mathrm{to}\:\mathrm{PO}. \\ $$

Question Number 59282 Answers: 1 Comments: 1

calculate f(x)=∫_0 ^∞ e^(−x[t]) sin([t])dt with x>0 2) calculate ∫_0 ^∞ e^(−3[t]) sin([t])dt .

$${calculate}\:{f}\left({x}\right)=\int_{\mathrm{0}} ^{\infty} \:\:{e}^{−{x}\left[{t}\right]} {sin}\left(\left[{t}\right]\right){dt} \\ $$$${with}\:{x}>\mathrm{0} \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:\int_{\mathrm{0}} ^{\infty} \:\:{e}^{−\mathrm{3}\left[{t}\right]} {sin}\left(\left[{t}\right]\right){dt}\:. \\ $$

Question Number 59280 Answers: 0 Comments: 0

find Σ_(n=1) ^∞ (([(√(n+1))]−[(√n)])/n^2 )

$${find}\:\sum_{{n}=\mathrm{1}} ^{\infty} \:\frac{\left[\sqrt{{n}+\mathrm{1}}\right]−\left[\sqrt{{n}}\right]}{{n}^{\mathrm{2}} } \\ $$

Question Number 59279 Answers: 0 Comments: 5

find ∫_0 ^(π/2) (x/(sinx))dx

$${find}\:\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:\:\:\frac{{x}}{{sinx}}{dx} \\ $$

Question Number 59278 Answers: 0 Comments: 3

let f(x) =∫_0 ^∞ ((ln(1+xt^2 ))/(2+t^2 )) dt determine a explicit form of f(x) 2)calculate ∫_0 ^∞ ((ln(1+3x^2 ))/(2+t^2 ))dt

$${let}\:{f}\left({x}\right)\:=\int_{\mathrm{0}} ^{\infty} \:\:\frac{{ln}\left(\mathrm{1}+{xt}^{\mathrm{2}} \right)}{\mathrm{2}+{t}^{\mathrm{2}} }\:{dt} \\ $$$${determine}\:{a}\:{explicit}\:{form}\:{of}\:{f}\left({x}\right) \\ $$$$\left.\mathrm{2}\right){calculate}\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{{ln}\left(\mathrm{1}+\mathrm{3}{x}^{\mathrm{2}} \right)}{\mathrm{2}+{t}^{\mathrm{2}} }{dt} \\ $$

Question Number 59277 Answers: 0 Comments: 1

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

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

Question Number 59276 Answers: 0 Comments: 0

find the value of Σ_(n=2) ^∞ (n/((n−1)^3 (n+1)^3 ))

$${find}\:{the}\:{value}\:{of}\:\:\sum_{{n}=\mathrm{2}} ^{\infty} \:\:\frac{{n}}{\left({n}−\mathrm{1}\right)^{\mathrm{3}} \left({n}+\mathrm{1}\right)^{\mathrm{3}} } \\ $$

Question Number 59275 Answers: 0 Comments: 3

let f(x)=∫_0 ^1 ln(1+xe^(−t) )dt 1)find a explicit form of f(x) 2)calculate ∫_0 ^1 ln(1+2e^(−t) )dt 3) developp f(x)at integr serie if ∣x∣<1

$${let}\:{f}\left({x}\right)=\int_{\mathrm{0}} ^{\mathrm{1}} {ln}\left(\mathrm{1}+{xe}^{−{t}} \right){dt} \\ $$$$\left.\mathrm{1}\right){find}\:{a}\:{explicit}\:{form}\:{of}\:{f}\left({x}\right) \\ $$$$\left.\mathrm{2}\right){calculate}\:\int_{\mathrm{0}} ^{\mathrm{1}} {ln}\left(\mathrm{1}+\mathrm{2}{e}^{−{t}} \right){dt} \\ $$$$\left.\mathrm{3}\right)\:{developp}\:{f}\left({x}\right){at}\:{integr}\:{serie}\:{if}\:\mid{x}\mid<\mathrm{1} \\ $$

Question Number 59274 Answers: 1 Comments: 2

calculate ∫_0 ^1 arctan(1+x+x^2 )dx

$${calculate}\:\int_{\mathrm{0}} ^{\mathrm{1}} {arctan}\left(\mathrm{1}+{x}+{x}^{\mathrm{2}} \right){dx} \\ $$

Question Number 59273 Answers: 1 Comments: 0

abc = 64 a, b, c ∈ R^+ Find K that satisfy to the inequality : (((a + b) (√(ab)) + (b + c) (√(bc)) + (c + a) (√(ca)))/(√(abc))) ≥ (√a) + (√b) + (√c) + K .

$${abc}\:\:=\:\:\mathrm{64} \\ $$$${a},\:{b},\:{c}\:\:\in\:\:\mathbb{R}^{+} \\ $$$${Find}\:\:{K}\:\:{that}\:\:{satisfy}\:\:{to}\:\:{the}\:\:{inequality}\:\:: \\ $$$$\:\:\:\:\:\frac{\left({a}\:+\:{b}\right)\:\sqrt{{ab}}\:\:+\:\:\left({b}\:+\:{c}\right)\:\sqrt{{bc}}\:\:+\:\:\left({c}\:+\:{a}\right)\:\sqrt{{ca}}}{\sqrt{{abc}}}\:\:\:\geqslant\:\:\sqrt{{a}}\:\:+\:\:\sqrt{{b}}\:\:+\:\:\sqrt{{c}}\:\:+\:\:{K}\:\:. \\ $$

Question Number 59270 Answers: 1 Comments: 0

Solve the equation 3x^(1/2) +5−2x^(1/2) =0

$$\mathrm{Solve}\:\mathrm{the}\:\mathrm{equation}\:\mathrm{3x}^{\frac{\mathrm{1}}{\mathrm{2}}} +\mathrm{5}−\mathrm{2x}^{\frac{\mathrm{1}}{\mathrm{2}}} =\mathrm{0} \\ $$

Question Number 59342 Answers: 1 Comments: 0

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