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Question Number 101248 Answers: 0 Comments: 0

Π_(p∈P/(2..3)) ((1/p))^2 =? p is prime number Any help ?

$$\:\:\:\underset{\boldsymbol{{p}}\in\boldsymbol{{P}}/\left(\mathrm{2}..\mathrm{3}\right)} {\prod}\left(\frac{\mathrm{1}}{\boldsymbol{{p}}}\right)^{\mathrm{2}} =?\:\:\:\:\:\boldsymbol{{p}}\:{is}\:{prime}\:{number} \\ $$$${Any}\:{help}\:? \\ $$

Question Number 101247 Answers: 1 Comments: 0

Question Number 101243 Answers: 0 Comments: 3

Find the solution xa^(1/x) +(1/x)a^x =2a a∈{−1,0,1} and also find when a is not given

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{solution}\: \\ $$$$\:\:\mathrm{xa}^{\frac{\mathrm{1}}{\mathrm{x}}} +\frac{\mathrm{1}}{\mathrm{x}}\mathrm{a}^{\mathrm{x}} =\mathrm{2a}\:\:\:\mathrm{a}\in\left\{−\mathrm{1},\mathrm{0},\mathrm{1}\right\}\:\:\:{and}\:{also}\:{find}\:{when}\:{a}\:\:{is}\:{not}\:{given} \\ $$

Question Number 101307 Answers: 0 Comments: 5

Some comments with inapproriate language were deleted. Kindly refrain from posting abusive comments. Forum has been around for a long time without these occurrences. Every new user, please scroll through the previous posts and abide by the established conventions followed by everyone else.

$$\mathrm{Some}\:\mathrm{comments}\:\mathrm{with}\:\mathrm{inapproriate} \\ $$$$\mathrm{language}\:\mathrm{were}\:\mathrm{deleted}. \\ $$$$\mathrm{Kindly}\:\mathrm{refrain}\:\mathrm{from}\:\mathrm{posting}\:\mathrm{abusive} \\ $$$$\mathrm{comments}.\:\mathrm{Forum}\:\mathrm{has}\:\mathrm{been}\:\mathrm{around} \\ $$$$\mathrm{for}\:\mathrm{a}\:\mathrm{long}\:\mathrm{time}\:\mathrm{without}\:\mathrm{these} \\ $$$$\mathrm{occurrences}. \\ $$$$\mathrm{Every}\:\mathrm{new}\:\mathrm{user},\:\mathrm{please}\:\mathrm{scroll}\:\mathrm{through} \\ $$$$\mathrm{the}\:\mathrm{previous}\:\mathrm{posts}\:\mathrm{and}\:\mathrm{abide}\:\mathrm{by}\:\mathrm{the}\: \\ $$$$\mathrm{established}\:\mathrm{conventions}\:\mathrm{followed}\:\mathrm{by}\: \\ $$$$\mathrm{everyone}\:\mathrm{else}. \\ $$

Question Number 101239 Answers: 1 Comments: 0

lim_(x→∞) (((1+(1/2)+(1/3)+......+(1/n))/(1+(1/3)+(1/5)......+(1/(2n+1)))))

$$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\left(\frac{\mathrm{1}+\frac{\mathrm{1}}{\mathrm{2}}+\frac{\mathrm{1}}{\mathrm{3}}+......+\frac{\mathrm{1}}{{n}}}{\mathrm{1}+\frac{\mathrm{1}}{\mathrm{3}}+\frac{\mathrm{1}}{\mathrm{5}}......+\frac{\mathrm{1}}{\mathrm{2}{n}+\mathrm{1}}}\right) \\ $$

Question Number 101234 Answers: 0 Comments: 0

Show that the greatest integer function is Riemann integrable within all segments of R

$$\mathcal{S}\mathrm{how}\:\mathrm{that}\:\mathrm{the}\:\mathrm{greatest}\:\mathrm{integer}\:\mathrm{function}\:\mathrm{is}\:\mathrm{Riemann} \\ $$$$\mathrm{integrable}\:\mathrm{within}\:\mathrm{all}\:\mathrm{segments}\:\mathrm{of}\:\mathbb{R} \\ $$

Question Number 101231 Answers: 1 Comments: 1

Question Number 101225 Answers: 0 Comments: 4

Question Number 101220 Answers: 1 Comments: 0

∫∫_D (√(x^2 +y^2 ))dxdy D= { (((x,y)∈R, x^2 +y^2 ≥2y, x^2 +y^2 ≤1)),((x≥0 , y≥0)) :}

$$\int\int_{\mathrm{D}} \sqrt{\mathrm{x}^{\mathrm{2}} +\mathrm{y}^{\mathrm{2}} }\mathrm{dxdy}\:\:\:\mathcal{D}=\begin{cases}{\left(\mathrm{x},\mathrm{y}\right)\in\mathbb{R},\:\mathrm{x}^{\mathrm{2}} +\mathrm{y}^{\mathrm{2}} \geqslant\mathrm{2y},\:\mathrm{x}^{\mathrm{2}} +\mathrm{y}^{\mathrm{2}} \leqslant\mathrm{1}}\\{\mathrm{x}\geqslant\mathrm{0}\:,\:\mathrm{y}\geqslant\mathrm{0}}\end{cases} \\ $$

Question Number 101303 Answers: 1 Comments: 1

i^i^(i.∞) =?

$${i}^{{i}^{{i}.\infty} } =? \\ $$

Question Number 101293 Answers: 1 Comments: 8

Question Number 101291 Answers: 1 Comments: 0

Question Number 101285 Answers: 0 Comments: 1

∫(((x^m −x^n ))/(√x))dx=?

$$\int\frac{\left(\mathrm{x}^{\mathrm{m}} −\mathrm{x}^{\mathrm{n}} \right)}{\sqrt{\mathrm{x}}}\mathrm{dx}=? \\ $$

Question Number 101278 Answers: 0 Comments: 2

Did I miss some updates? Do we get a prize or at least an award for the fastest answer? Or for the “best”, or for the most sophisticated answer? Or for using the largest font size and the brightest colour? Annoying developments...

$$\mathrm{Did}\:\mathrm{I}\:\mathrm{miss}\:\mathrm{some}\:\mathrm{updates}? \\ $$$$\mathrm{Do}\:\mathrm{we}\:\mathrm{get}\:\mathrm{a}\:\mathrm{prize}\:\mathrm{or}\:\mathrm{at}\:\mathrm{least}\:\mathrm{an}\:\mathrm{award}\:\mathrm{for}\:\mathrm{the} \\ $$$$\mathrm{fastest}\:\mathrm{answer}?\:\mathrm{Or}\:\mathrm{for}\:\mathrm{the}\:``\mathrm{best}'',\:\mathrm{or}\:\mathrm{for}\:\mathrm{the} \\ $$$$\mathrm{most}\:\mathrm{sophisticated}\:\mathrm{answer}?\:\mathrm{Or}\:\mathrm{for}\:\mathrm{using}\:\mathrm{the} \\ $$$$\mathrm{largest}\:\mathrm{font}\:\mathrm{size}\:\mathrm{and}\:\mathrm{the}\:\mathrm{brightest}\:\mathrm{colour}? \\ $$$$\mathrm{Annoying}\:\mathrm{developments}... \\ $$

Question Number 101277 Answers: 2 Comments: 0

∫_0 ^1 (((x−1) dx )/((x+1)ln (x)))

$$\underset{\mathrm{0}} {\overset{\mathrm{1}} {\int}}\:\frac{\left({x}−\mathrm{1}\right)\:{dx}\:}{\left({x}+\mathrm{1}\right)\mathrm{ln}\:\left({x}\right)} \\ $$$$ \\ $$

Question Number 101156 Answers: 1 Comments: 0

Find the range of the function: h : x = 2 − x^2 sin(x), x ≥ 0

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{range}\:\mathrm{of}\:\mathrm{the}\:\mathrm{function}: \\ $$$$\:\:\:\:\:\mathrm{h}\::\:\mathrm{x}\:\:\:=\:\:\mathrm{2}\:\:−\:\:\mathrm{x}^{\mathrm{2}} \:\mathrm{sin}\left(\mathrm{x}\right),\:\:\:\:\:\:\mathrm{x}\:\:\geqslant\:\:\mathrm{0} \\ $$

Question Number 101212 Answers: 2 Comments: 1

∫e^x sin x dx = −e^x cos x + e^x sin x − ∫ e^x sin x dx

$$\int{e}^{{x}} \mathrm{sin}\:{x}\:{dx}\:=\:−{e}^{{x}} {cos}\:{x}\:+\:{e}^{{x}} \:{sin}\:{x}\:−\:\int\:{e}^{{x}} \:\mathrm{sin}\:\:{x}\:{dx} \\ $$

Question Number 101148 Answers: 0 Comments: 2

lim_(x→0) ((sin (ln (1+x))−ln(1+sin x))/(sin^4 ((x/2)))) =?

$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\mathrm{sin}\:\left(\mathrm{ln}\:\left(\mathrm{1}+\mathrm{x}\right)\right)−\mathrm{ln}\left(\mathrm{1}+\mathrm{sin}\:\mathrm{x}\right)}{\mathrm{sin}\:^{\mathrm{4}} \left(\frac{\mathrm{x}}{\mathrm{2}}\right)}\:=?\: \\ $$

Question Number 101192 Answers: 1 Comments: 2

∫ (x/(1+sin x)) dx

$$\int\:\frac{{x}}{\mathrm{1}+\mathrm{sin}\:{x}}\:{dx}\: \\ $$

Question Number 101185 Answers: 2 Comments: 0

In an arithmetic progression the sum of the third term and 8th term is 49 and the sum of the 5th and 9th term is 58.Find the first term and the common difference using simultaneous equations.

$${In}\:{an}\:{arithmetic}\:{progression}\:{the}\:{sum}\:{of}\:{the}\:{third}\:{term}\:{and}\:\mathrm{8}{th}\:{term}\:{is}\:\mathrm{49}\:{and}\:{the}\:{sum}\:{of}\:{the}\:\:\mathrm{5}{th}\:{and}\:\mathrm{9}{th}\:{term}\:{is}\:\mathrm{58}.{Find}\:{the}\:{first}\:{term}\:{and}\:{the}\:{common}\:{difference}\:{using}\:{simultaneous}\:{equations}. \\ $$

Question Number 101183 Answers: 1 Comments: 0