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Question Number 42593 Answers: 1 Comments: 1

Question Number 42592 Answers: 1 Comments: 0

Question Number 42583 Answers: 0 Comments: 6

Question Number 42580 Answers: 1 Comments: 1

Question Number 42579 Answers: 1 Comments: 1

∫ sinx/(√(1+sinx))

$$\int\:{sinx}/\sqrt{\mathrm{1}+{sinx}} \\ $$

Question Number 42559 Answers: 5 Comments: 0

Question Number 42553 Answers: 0 Comments: 1

Question Number 42550 Answers: 1 Comments: 3

2^(1/x) =(√x) Find x

$$\mathrm{2}^{\frac{\mathrm{1}}{{x}}} =\sqrt{{x}} \\ $$$${Find}\:{x} \\ $$

Question Number 43535 Answers: 2 Comments: 2

1) find the value of ∫_(π/4) ^(π/3) (√(1+tanθ))dθ .

$$\left.\mathrm{1}\right)\:{find}\:{the}\:{value}\:{of}\:\:\int_{\frac{\pi}{\mathrm{4}}} ^{\frac{\pi}{\mathrm{3}}} \:\sqrt{\mathrm{1}+{tan}\theta}{d}\theta\:. \\ $$

Question Number 42549 Answers: 1 Comments: 0

If y = a^(1/(1 − log_a x)) and z = a^(1/(1 − log_a y)) . show that x = a^(1/(1 − log_a z))

$$\mathrm{If}\:\:\:\mathrm{y}\:=\:\mathrm{a}^{\frac{\mathrm{1}}{\mathrm{1}\:−\:\mathrm{log}_{\mathrm{a}} \mathrm{x}}} \:\:\:\:\:\mathrm{and}\:\:\:\:\:\:\:\:\mathrm{z}\:=\:\mathrm{a}^{\frac{\mathrm{1}}{\mathrm{1}\:−\:\mathrm{log}_{\mathrm{a}} \mathrm{y}}} \:\:.\:\:\mathrm{show}\:\mathrm{that}\:\:\:\:\:\mathrm{x}\:=\:\mathrm{a}^{\frac{\mathrm{1}}{\mathrm{1}\:−\:\mathrm{log}_{\mathrm{a}} \mathrm{z}}} \\ $$

Question Number 42543 Answers: 0 Comments: 3

Question Number 42538 Answers: 1 Comments: 1

Question Number 43537 Answers: 0 Comments: 1

let S_n =Σ_(k=1) ^n (e^(k/n) /n) find lim_(n→+∞) S_n

$${let}\:{S}_{{n}} =\sum_{{k}=\mathrm{1}} ^{{n}} \:\:\frac{{e}^{\frac{{k}}{{n}}} }{{n}} \\ $$$${find}\:{lim}_{{n}\rightarrow+\infty} {S}_{{n}} \\ $$

Question Number 42521 Answers: 1 Comments: 0

Let a^(→ ) , b^→ , c^→ be three unit vectors such that 3a^→ +4b^→ +5c^→ = 0. Then prove that a^(→ ) , b^→ ,c^→ are coplanar.

$$\mathrm{Let}\:\overset{\rightarrow\:} {\mathrm{a}},\:\overset{\rightarrow} {\mathrm{b}}\:,\:\overset{\rightarrow} {\mathrm{c}}\:\mathrm{be}\:\mathrm{three}\:\mathrm{unit}\:\mathrm{vectors} \\ $$$$\mathrm{such}\:\mathrm{that}\:\mathrm{3}\overset{\rightarrow} {\mathrm{a}}+\mathrm{4}\overset{\rightarrow} {\mathrm{b}}+\mathrm{5}\overset{\rightarrow} {\mathrm{c}}\:=\:\mathrm{0}.\:\mathrm{Then}\:\mathrm{prove} \\ $$$$\mathrm{that}\:\overset{\rightarrow\:} {\mathrm{a}},\:\overset{\rightarrow} {\mathrm{b}},\overset{\rightarrow} {\mathrm{c}}\:\mathrm{are}\:\mathrm{coplanar}. \\ $$

Question Number 42520 Answers: 1 Comments: 0

cos^3 A.sin3A+sinA.cos3A=(3/4)sin4A

$${cos}^{\mathrm{3}} \:{A}.{sin}\mathrm{3}{A}+{sinA}.{cos}\mathrm{3}{A}=\frac{\mathrm{3}}{\mathrm{4}}{sin}\mathrm{4}{A} \\ $$

Question Number 42519 Answers: 1 Comments: 0

cosec2A+cosec4A+cosec8A=cotA−cot8A(prlve ghis)

$${cosec}\mathrm{2}{A}+{cosec}\mathrm{4}{A}+{cosec}\mathrm{8}{A}={cotA}−{cot}\mathrm{8}{A}\left({prlve}\:{ghis}\right) \\ $$

Question Number 42516 Answers: 1 Comments: 1

(x−(1/2)a),(x−(5/2)a)=? Solve Please.

$$\left(\mathrm{x}−\frac{\mathrm{1}}{\mathrm{2}}\mathrm{a}\right),\left(\mathrm{x}−\frac{\mathrm{5}}{\mathrm{2}}\mathrm{a}\right)=? \\ $$$$\mathrm{Solve}\:\mathrm{Please}. \\ $$

Question Number 42514 Answers: 1 Comments: 0

calculate d(x!)/dx= ?

$${calculate}\:\:{d}\left({x}!\right)/{dx}=\:? \\ $$

Question Number 42508 Answers: 2 Comments: 0

find the value of A =cos((π/5)).cos(((2π)/5)) cos(((4π)/5)) and B =sin((π/5))sin(((2π)/5))sin(((4π)/5)).

$${find}\:{the}\:{value}\:{of}\: \\ $$$${A}\:={cos}\left(\frac{\pi}{\mathrm{5}}\right).{cos}\left(\frac{\mathrm{2}\pi}{\mathrm{5}}\right)\:{cos}\left(\frac{\mathrm{4}\pi}{\mathrm{5}}\right)\:{and}\:{B}\:={sin}\left(\frac{\pi}{\mathrm{5}}\right){sin}\left(\frac{\mathrm{2}\pi}{\mathrm{5}}\right){sin}\left(\frac{\mathrm{4}\pi}{\mathrm{5}}\right). \\ $$

Question Number 42507 Answers: 0 Comments: 2

let j =e^((i2π)/3) and p(x) =(1+xj)^n −(1−xj)^n 1) find the roots of p(x) and factorize inside C[x] p(x) 2) decompose inside C(x) the fration F(x) =(1/(p(x))) .

$${let}\:{j}\:={e}^{\frac{{i}\mathrm{2}\pi}{\mathrm{3}}} \:\:\:{and}\:\:\:{p}\left({x}\right)\:=\left(\mathrm{1}+{xj}\right)^{{n}} \:−\left(\mathrm{1}−{xj}\right)^{{n}} \\ $$$$\left.\mathrm{1}\right)\:{find}\:{the}\:{roots}\:{of}\:{p}\left({x}\right)\:{and}\:{factorize}\:{inside}\:{C}\left[{x}\right]\:{p}\left({x}\right) \\ $$$$\left.\mathrm{2}\right)\:{decompose}\:{inside}\:{C}\left({x}\right)\:{the}\:{fration}\:{F}\left({x}\right)\:=\frac{\mathrm{1}}{{p}\left({x}\right)}\:. \\ $$

Question Number 42506 Answers: 0 Comments: 1

find the value of ∫_0 ^∞ ((ln(t))/((^3 (√t^2 ))(1+t)))dt .

$${find}\:{the}\:{value}\:{of}\:\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{{ln}\left({t}\right)}{\left(^{\mathrm{3}} \sqrt{{t}^{\mathrm{2}} }\right)\left(\mathrm{1}+{t}\right)}{dt}\:. \\ $$

Question Number 42505 Answers: 0 Comments: 2

calculate ∫_0 ^∞ ((ln(t))/((1+t)(√t))) dt .

$${calculate}\:\:\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{{ln}\left({t}\right)}{\left(\mathrm{1}+{t}\right)\sqrt{{t}}}\:{dt}\:. \\ $$

Question Number 42504 Answers: 0 Comments: 1

let x>0 prove that ∫_0 ^∞ ((e^(−t^2 ) ln(1+xt^2 ))/t^2 ) dt =π ∫_0 ^(√x) e^(1/u^2 ) du .

$${let}\:{x}>\mathrm{0}\:{prove}\:{that} \\ $$$$\int_{\mathrm{0}} ^{\infty} \:\:\:\:\frac{{e}^{−{t}^{\mathrm{2}} } {ln}\left(\mathrm{1}+{xt}^{\mathrm{2}} \right)}{{t}^{\mathrm{2}} }\:{dt}\:=\pi\:\int_{\mathrm{0}} ^{\sqrt{{x}}} \:\:{e}^{\frac{\mathrm{1}}{{u}^{\mathrm{2}} }} \:\:{du}\:. \\ $$

Question Number 42503 Answers: 1 Comments: 1

calculate ∫_(−∞) ^(+∞) (dx/(1+x^2 +x^4 ))

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

Question Number 42502 Answers: 0 Comments: 0

calculate A_n = ∫_0 ^(2π) ((cos(nx))/(cosx +sinx))dx with n from N

$${calculate}\:{A}_{{n}} =\:\int_{\mathrm{0}} ^{\mathrm{2}\pi} \:\:\frac{{cos}\left({nx}\right)}{{cosx}\:+{sinx}}{dx}\:\:{with}\:{n}\:{from}\:{N} \\ $$

Question Number 42501 Answers: 0 Comments: 1

calculate I = ∫_0 ^(2π) ((cos(4x))/(cosx +sinx)) and J = ∫_0 ^(2π) ((sin(4x))/(cosx +sinx))dx

$${calculate}\:{I}\:=\:\int_{\mathrm{0}} ^{\mathrm{2}\pi} \:\:\:\frac{{cos}\left(\mathrm{4}{x}\right)}{{cosx}\:+{sinx}}\:\:{and}\:{J}\:=\:\int_{\mathrm{0}} ^{\mathrm{2}\pi} \:\:\frac{{sin}\left(\mathrm{4}{x}\right)}{{cosx}\:+{sinx}}{dx} \\ $$

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