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Question Number 109190 Answers: 0 Comments: 0

Question Number 109178 Answers: 2 Comments: 1

Question Number 109174 Answers: 1 Comments: 0

Question Number 109169 Answers: 1 Comments: 0

The value of 1∙1! + 2∙2! + 3∙3! +...+n∙n! is

$$\mathrm{The}\:\mathrm{value}\:\mathrm{of}\:\:\mathrm{1}\centerdot\mathrm{1}!\:+\:\mathrm{2}\centerdot\mathrm{2}!\:+\:\mathrm{3}\centerdot\mathrm{3}!\:+...+{n}\centerdot{n}! \\ $$$$\mathrm{is}\: \\ $$

Question Number 109167 Answers: 1 Comments: 0

Question Number 109160 Answers: 4 Comments: 0

Find the equation of line through the point of intersection of the line x+3y−11=0 and 5x−4y+2=0 and perpendicular to 4x+2y+9=0.

$${Find}\:{the}\:{equation}\:{of}\:{line}\:{through} \\ $$$${the}\:{point}\:{of}\:{intersection}\:{of}\:{the} \\ $$$${line}\:{x}+\mathrm{3}{y}−\mathrm{11}=\mathrm{0}\:{and}\:\mathrm{5}{x}−\mathrm{4}{y}+\mathrm{2}=\mathrm{0} \\ $$$${and}\:{perpendicular}\:{to}\:\mathrm{4}{x}+\mathrm{2}{y}+\mathrm{9}=\mathrm{0}. \\ $$

Question Number 109149 Answers: 0 Comments: 2

if f:x→x be a mapping prove that (f⊆I_X ∨I_X ⊆f)→f=I_(X ) ? help me sir

$${if}\:{f}:{x}\rightarrow{x}\:{be}\:{a}\:{mapping}\:{prove}\:{that}\:\left({f}\subseteq{I}_{{X}} \vee{I}_{{X}} \subseteq{f}\right)\rightarrow{f}={I}_{{X}\:} ? \\ $$$${help}\:{me}\:{sir} \\ $$

Question Number 109147 Answers: 3 Comments: 0

The principal argument of z=1+cos (((6π)/5))+isin (((6π)/5)) is = ?

$${The}\:{principal}\:{argument}\:{of} \\ $$$${z}=\mathrm{1}+\mathrm{cos}\:\left(\frac{\mathrm{6}\pi}{\mathrm{5}}\right)+{i}\mathrm{sin}\:\left(\frac{\mathrm{6}\pi}{\mathrm{5}}\right)\:\:\:{is}\:=\:? \\ $$

Question Number 109145 Answers: 0 Comments: 0

Question Number 109144 Answers: 0 Comments: 0

Question Number 109143 Answers: 0 Comments: 0

Question Number 109142 Answers: 0 Comments: 1

Question Number 109141 Answers: 2 Comments: 0

Question Number 109139 Answers: 0 Comments: 1

lim_(x→−∞) (1−x) sin ∣2x−2∣ ?

$$\:\underset{{x}\rightarrow−\infty} {\mathrm{lim}}\:\left(\mathrm{1}−{x}\right)\:\mathrm{sin}\:\mid\mathrm{2}{x}−\mathrm{2}\mid\:? \\ $$

Question Number 109136 Answers: 1 Comments: 0

∫_0 ^(1/2) ((ln(1-t)ln(t))/t) dt I′m about to give up

$$\int_{\mathrm{0}} ^{\mathrm{1}/\mathrm{2}} \frac{{ln}\left(\mathrm{1}-{t}\right){ln}\left({t}\right)}{{t}}\:{dt} \\ $$$${I}'{m}\:{about}\:{to}\:{give}\:{up} \\ $$

Question Number 109237 Answers: 4 Comments: 0

((♭o♭hans)/(∠∠∠∠∠)) { ((x^3 +x^2 y = 9)),((y^3 +y^2 x = 25)) :}. find x and y.

$$\:\:\frac{\flat{o}\flat{hans}}{\angle\angle\angle\angle\angle} \\ $$$$\begin{cases}{{x}^{\mathrm{3}} +{x}^{\mathrm{2}} {y}\:=\:\mathrm{9}}\\{{y}^{\mathrm{3}} +{y}^{\mathrm{2}} {x}\:=\:\mathrm{25}}\end{cases}.\:{find}\:{x}\:{and}\:{y}. \\ $$

Question Number 109129 Answers: 1 Comments: 0

∫_0 ^(π/2) ((ln (cos x)ln (sin x))/(tan x)) dx

$$\:\underset{\mathrm{0}} {\overset{\pi/\mathrm{2}} {\int}}\:\frac{\mathrm{ln}\:\left(\mathrm{cos}\:{x}\right)\mathrm{ln}\:\left(\mathrm{sin}\:{x}\right)}{\mathrm{tan}\:{x}}\:{dx} \\ $$

Question Number 109128 Answers: 0 Comments: 1

A high school question from Japan Let P(x) be a real polynomial of degree 4 and P^((4)) (0)=72. If there exists t∈R and m,n∈R such that P′′(t)=0 and P′(t)=P′(t+m)=∫_t ^( t+m) P′(x)dx=n ⇒Find the value of m and n.

$$\mathrm{A}\:\mathrm{high}\:\mathrm{school}\:\mathrm{question}\:\mathrm{from}\:\mathrm{Japan} \\ $$$$ \\ $$$$\mathrm{Let}\:\mathrm{P}\left({x}\right)\:\mathrm{be}\:\mathrm{a}\:\mathrm{real}\:\mathrm{polynomial}\:\mathrm{of}\:\mathrm{degree}\:\mathrm{4}\: \\ $$$$\mathrm{and}\:\mathrm{P}^{\left(\mathrm{4}\right)} \left(\mathrm{0}\right)=\mathrm{72}. \\ $$$$\mathrm{If}\:\mathrm{there}\:\mathrm{exists}\:{t}\in\mathbb{R}\:\mathrm{and}\:{m},{n}\in\mathbb{R}\:\mathrm{such}\:\mathrm{that} \\ $$$$\mathrm{P}''\left({t}\right)=\mathrm{0}\:\mathrm{and}\:\mathrm{P}'\left({t}\right)=\mathrm{P}'\left({t}+{m}\right)=\int_{{t}} ^{\:{t}+{m}} \mathrm{P}'\left({x}\right){dx}={n} \\ $$$$\Rightarrow\mathrm{Find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:{m}\:\mathrm{and}\:{n}. \\ $$

Question Number 109123 Answers: 0 Comments: 0

prove that : ∫_(π/4) ^((3π)/4) sin(x)−cos(x)dx ≥∫_π ^((3π)/2) sin(x)+cos(x)dx

$${prove}\:{that}\:: \\ $$$$\int_{\frac{\pi}{\mathrm{4}}} ^{\frac{\mathrm{3}\pi}{\mathrm{4}}} {sin}\left({x}\right)−{cos}\left({x}\right){dx}\:\geqslant\int_{\pi} ^{\frac{\mathrm{3}\pi}{\mathrm{2}}} {sin}\left({x}\right)+{cos}\left({x}\right){dx} \\ $$

Question Number 109119 Answers: 2 Comments: 0

if f(x^2 )=y ,f′(x)=(√(5x−1 )) then (dy/dx)=.....

$${if}\:{f}\left({x}^{\mathrm{2}} \right)={y}\:\:,{f}'\left({x}\right)=\sqrt{\mathrm{5}{x}−\mathrm{1}\:}\:{then}\: \\ $$$$\frac{{dy}}{{dx}}=..... \\ $$

Question Number 109117 Answers: 1 Comments: 0

Question Number 109116 Answers: 3 Comments: 0

∫_0 ^∞ ((ln(x))/((1+x)^4 )) Please help

$$\int_{\mathrm{0}} ^{\infty} \frac{{ln}\left({x}\right)}{\left(\mathrm{1}+{x}\right)^{\mathrm{4}} } \\ $$$${Please}\:{help} \\ $$

Question Number 109101 Answers: 3 Comments: 0

Given a function f(x+3)=f(x) for ∀x∈R. If ∫_(−3) ^6 f(x)dx = −6 then ∫_3 ^9 f(x) dx = ?

$$\:{Given}\:{a}\:{function}\:{f}\left({x}+\mathrm{3}\right)={f}\left({x}\right) \\ $$$${for}\:\forall{x}\in\mathbb{R}.\:{If}\:\underset{−\mathrm{3}} {\overset{\mathrm{6}} {\int}}{f}\left({x}\right){dx}\:=\:−\mathrm{6}\: \\ $$$${then}\:\underset{\mathrm{3}} {\overset{\mathrm{9}} {\int}}{f}\left({x}\right)\:{dx}\:=\:? \\ $$

Question Number 109097 Answers: 1 Comments: 0

((♭o♭hans)/(∼∼∼∼∼)) ∫_1 ^2 x sec^(−1) (x)dx=?

$$\:\:\frac{\boldsymbol{\flat{o}\flat{hans}}}{\sim\sim\sim\sim\sim} \\ $$$$\underset{\mathrm{1}} {\overset{\mathrm{2}} {\int}}{x}\:\mathrm{sec}^{−\mathrm{1}} \left({x}\right){dx}=? \\ $$

Question Number 109091 Answers: 2 Comments: 0

((△♭eMath▽)/(≡⊸≡⊸≡)) lim_(x→π) ((sin x)/( (√(π+tan x))−(√(π−tan x)))) ?

$$\:\:\:\:\frac{\bigtriangleup\flat{e}\mathscr{M}{ath}\bigtriangledown}{\equiv\multimap\equiv\multimap\equiv} \\ $$$$\:\underset{{x}\rightarrow\pi} {\mathrm{lim}}\:\frac{\mathrm{sin}\:{x}}{\:\sqrt{\pi+\mathrm{tan}\:{x}}−\sqrt{\pi−\mathrm{tan}\:{x}}}\:? \\ $$

Question Number 109090 Answers: 1 Comments: 0

Find all those roots of the equation z^(12) −56z^6 −512=0 whose imaginary part is positive.

$${Find}\:{all}\:{those}\:{roots}\:{of}\:{the}\:{equation} \\ $$$$\:\boldsymbol{{z}}^{\mathrm{12}} −\mathrm{56}\boldsymbol{{z}}^{\mathrm{6}} −\mathrm{512}=\mathrm{0}\:\:{whose}\:{imaginary} \\ $$$${part}\:{is}\:{positive}. \\ $$

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