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Question Number 114812 Answers: 3 Comments: 0

Show that arcsin((√x))=(π/4)+(1/2)arcsin(2x−1)

$$\mathrm{Show}\:\mathrm{that}\: \\ $$$$\mathrm{arcsin}\left(\sqrt{\mathrm{x}}\right)=\frac{\pi}{\mathrm{4}}+\frac{\mathrm{1}}{\mathrm{2}}\mathrm{arcsin}\left(\mathrm{2x}−\mathrm{1}\right) \\ $$

Question Number 114809 Answers: 1 Comments: 1

{ ((1−((12)/(y+3x))=(2/( (√x))))),((1+((12)/(y+3x))=(6/( (√y))))) :}

$$\begin{cases}{\mathrm{1}−\frac{\mathrm{12}}{{y}+\mathrm{3}{x}}=\frac{\mathrm{2}}{\:\sqrt{{x}}}}\\{\mathrm{1}+\frac{\mathrm{12}}{{y}+\mathrm{3}{x}}=\frac{\mathrm{6}}{\:\sqrt{{y}}}}\end{cases} \\ $$

Question Number 114808 Answers: 1 Comments: 0

...nice math... evaluate :: I =∫_0 ^( (π/4)) ((ln(1+sin(x)))/(cos(x)))dx=??? ...m.n.july.1970...

$$\:\:\:\:\:\:...{nice}\:{math}... \\ $$$$ \\ $$$$\:\:\:\:\:{evaluate}\::: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{I}\:=\int_{\mathrm{0}} ^{\:\frac{\pi}{\mathrm{4}}} \frac{{ln}\left(\mathrm{1}+{sin}\left({x}\right)\right)}{{cos}\left({x}\right)}{dx}=???\: \\ $$$$ \\ $$$$...{m}.{n}.{july}.\mathrm{1970}... \\ $$$$\: \\ $$

Question Number 114807 Answers: 0 Comments: 7

is zero a natural number 0∈N?

$${is}\:{zero}\:{a}\:{natural}\:{number}\:\mathrm{0}\in\mathbb{N}? \\ $$

Question Number 114806 Answers: 1 Comments: 0

Question Number 114803 Answers: 0 Comments: 2

Question Number 114802 Answers: 1 Comments: 0

Question Number 114800 Answers: 1 Comments: 3

Question Number 114799 Answers: 1 Comments: 0

Question Number 114797 Answers: 1 Comments: 0

There are 6 people going to sit in a circle . The number of arrangements they sit if there are 2 people who always sit next to each other

$${There}\:{are}\:\mathrm{6}\:{people}\:{going}\:{to}\:{sit}\:{in}\: \\ $$$${a}\:{circle}\:.\:{The}\:{number}\:{of}\:{arrangements} \\ $$$${they}\:{sit}\:{if}\:{there}\:{are}\:\mathrm{2}\:{people}\:{who} \\ $$$${always}\:{sit}\:{next}\:{to}\:{each}\:{other} \\ $$

Question Number 114796 Answers: 2 Comments: 0

Question Number 114795 Answers: 1 Comments: 0

Question Number 114792 Answers: 0 Comments: 0

find the angle incilination of the line x+2y=−3 help me sir

$${find}\:{the}\:{angle}\:{incilination}\:{of}\:{the}\:{line}\:{x}+\mathrm{2}{y}=−\mathrm{3}\: \\ $$$${help}\:{me}\:{sir} \\ $$

Question Number 114790 Answers: 1 Comments: 0

lim_((x,y)→(0,0)) ((x^(3/2) y)/(x^3 +y^2 ))=?

$$\underset{\left({x},{y}\right)\rightarrow\left(\mathrm{0},\mathrm{0}\right)} {\mathrm{lim}}\:\frac{{x}^{\mathrm{3}/\mathrm{2}} {y}}{{x}^{\mathrm{3}} +{y}^{\mathrm{2}} }=? \\ $$

Question Number 114784 Answers: 1 Comments: 0

Question Number 114782 Answers: 0 Comments: 2

0^0 =?

$$\mathrm{0}^{\mathrm{0}} =? \\ $$

Question Number 114779 Answers: 1 Comments: 0

Question Number 114777 Answers: 1 Comments: 0

Question Number 114773 Answers: 1 Comments: 0

Evaluate: ∫ (1/(sin^5 x + cos^5 x)) dx

$$\: \\ $$$$\:\:\mathrm{Evaluate}:\:\:\int\:\frac{\mathrm{1}}{\mathrm{sin}^{\mathrm{5}} \mathrm{x}\:+\:\mathrm{cos}^{\mathrm{5}} \mathrm{x}}\:\mathrm{dx} \\ $$

Question Number 114768 Answers: 2 Comments: 0

Solve for ∣x−2∣+∣1−x∣=4

$$\mathrm{Solve}\:\mathrm{for}\:\mid{x}−\mathrm{2}\mid+\mid\mathrm{1}−{x}\mid=\mathrm{4} \\ $$

Question Number 114765 Answers: 1 Comments: 0

Find the maximum. and minimum value of ⌊1+sinx⌋+⌊1+sin3x⌋+⌊1+sin2x⌋

$${Find}\:{the}\:\boldsymbol{{maximum}}.\:{and}\:\boldsymbol{{minimum}}\:{value}\:{of}\:\lfloor\mathrm{1}+{sinx}\rfloor+\lfloor\mathrm{1}+{sin}\mathrm{3}{x}\rfloor+\lfloor\mathrm{1}+{sin}\mathrm{2}{x}\rfloor \\ $$$$ \\ $$$$ \\ $$

Question Number 114764 Answers: 1 Comments: 0

Find period of f(x)=e^(cos^4 (πx)+x−⌊x⌋+cos^2 (πx))

$${Find}\:{period}\:{of}\:{f}\left({x}\right)={e}^{{cos}^{\mathrm{4}} \left(\pi{x}\right)+{x}−\lfloor{x}\rfloor+{cos}^{\mathrm{2}} \left(\pi{x}\right)} \\ $$$$ \\ $$

Question Number 114758 Answers: 1 Comments: 0

Π_(n=1) ^∞ ((4n^2 (10n−6)(10n−4))/((2n−1)^2 (10n−1)(10n+1))) =?

$$\underset{{n}=\mathrm{1}} {\overset{\infty} {\prod}}\:\frac{\mathrm{4}{n}^{\mathrm{2}} \left(\mathrm{10}{n}−\mathrm{6}\right)\left(\mathrm{10}{n}−\mathrm{4}\right)}{\left(\mathrm{2}{n}−\mathrm{1}\right)^{\mathrm{2}} \left(\mathrm{10}{n}−\mathrm{1}\right)\left(\mathrm{10}{n}+\mathrm{1}\right)}\:=? \\ $$

Question Number 114754 Answers: 4 Comments: 1

Without L′Hopital lim_(x→(π/4)) ((((1/(cos^2 x)) −2tan x ))/(cos 2x)) ?

$${Without}\:{L}'{Hopital}\: \\ $$$$\underset{{x}\rightarrow\frac{\pi}{\mathrm{4}}} {\mathrm{lim}}\:\frac{\left(\frac{\mathrm{1}}{\mathrm{cos}\:^{\mathrm{2}} {x}}\:−\mathrm{2tan}\:{x}\:\right)}{\mathrm{cos}\:\mathrm{2}{x}}\:? \\ $$

Question Number 114753 Answers: 1 Comments: 0

find minimum value of function f(x) = (((x+17)^3 )/x) , x>0

$${find}\:{minimum}\:{value}\:{of}\:{function} \\ $$$${f}\left({x}\right)\:=\:\frac{\left({x}+\mathrm{17}\right)^{\mathrm{3}} }{{x}}\:,\:{x}>\mathrm{0} \\ $$

Question Number 114740 Answers: 2 Comments: 0

question proposed by m.n july 1970 show that ∫_0 ^∞ ((ln(1+x))/(x(1+x^2 )))dx=((5π^2 )/(48))

$${question}\:{proposed}\:{by}\:{m}.{n}\:{july}\:\mathrm{1970} \\ $$$${show}\:{that} \\ $$$$\int_{\mathrm{0}} ^{\infty} \frac{\mathrm{ln}\left(\mathrm{1}+{x}\right)}{{x}\left(\mathrm{1}+{x}^{\mathrm{2}} \right)}{dx}=\frac{\mathrm{5}\pi^{\mathrm{2}} }{\mathrm{48}} \\ $$

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