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Question Number 106256 Answers: 0 Comments: 2

Question Number 106250 Answers: 0 Comments: 1

Question Number 106246 Answers: 3 Comments: 3

Question Number 106240 Answers: 1 Comments: 0

lim_(n→+∞) Σ_(k=1) ^n (((−1)^(k+1) )/k)=????

$$ \\ $$$$ \\ $$$$ \\ $$$$\boldsymbol{{li}}\underset{\boldsymbol{{n}}\rightarrow+\infty} {\boldsymbol{{m}}}\underset{{k}=\mathrm{1}} {\overset{{n}} {\sum}}\frac{\left(−\mathrm{1}\right)^{\boldsymbol{{k}}+\mathrm{1}} }{\boldsymbol{{k}}}=???? \\ $$

Question Number 106237 Answers: 1 Comments: 0

Question Number 106233 Answers: 2 Comments: 0

(x^2 + 1)(x − 1)^2 = 2017yz (y^2 + 1)(y − 1)^2 = 2017xz (z^2 + 1)(z − 1)^2 = 2017xy x ≥ 1 ; y ≥ 1 ; z ≥ 1 prove that x = y = z = ((1+ (√(2018)) + (√(2015+ 2(√(2018)))))/2)

$$\left({x}^{\mathrm{2}} \:+\:\mathrm{1}\right)\left({x}\:−\:\mathrm{1}\right)^{\mathrm{2}} \:=\:\mathrm{2017}{yz} \\ $$$$\left({y}^{\mathrm{2}} \:+\:\mathrm{1}\right)\left({y}\:−\:\mathrm{1}\right)^{\mathrm{2}} \:=\:\mathrm{2017}{xz} \\ $$$$\left({z}^{\mathrm{2}} \:+\:\mathrm{1}\right)\left({z}\:−\:\mathrm{1}\right)^{\mathrm{2}} \:=\:\mathrm{2017}{xy} \\ $$$${x}\:\geqslant\:\mathrm{1}\:;\:{y}\:\geqslant\:\mathrm{1}\:;\:{z}\:\geqslant\:\mathrm{1} \\ $$$${prove}\:{that}\:\:\:{x}\:=\:{y}\:=\:{z}\:= \\ $$$$\frac{\mathrm{1}+\:\sqrt{\mathrm{2018}}\:+\:\sqrt{\mathrm{2015}+\:\mathrm{2}\sqrt{\mathrm{2018}}}}{\mathrm{2}} \\ $$

Question Number 106232 Answers: 0 Comments: 0

find ∫ cos^n x ch(nx)dx /with n integr

$$\mathrm{find}\:\int\:\mathrm{cos}^{\mathrm{n}} \mathrm{x}\:\mathrm{ch}\left(\mathrm{nx}\right)\mathrm{dx}\:/\mathrm{with}\:\mathrm{n}\:\mathrm{integr} \\ $$

Question Number 106222 Answers: 1 Comments: 5

Determine x & y such that: lcm(x,y)−gcd(x,y)=x+y.

$$\mathcal{D}{etermine}\:{x}\:\&\:{y}\:{such}\:{that}: \\ $$$$\mathrm{lcm}\left({x},{y}\right)−\mathrm{gcd}\left({x},{y}\right)={x}+{y}. \\ $$

Question Number 106217 Answers: 1 Comments: 0

If f(x)= ((sin x−x cos x)/x^2 ) and f(0)=0 when x = 0 ,what will be the value of lim_(t→0) ((∫_0 ^t f(x) dx)/t^2 )

$$\mathrm{If}\:\mathrm{f}\left(\mathrm{x}\right)=\:\frac{\mathrm{sin}\:\mathrm{x}−\mathrm{x}\:\mathrm{cos}\:\mathrm{x}}{\mathrm{x}^{\mathrm{2}} }\:\mathrm{and}\:\mathrm{f}\left(\mathrm{0}\right)=\mathrm{0}\:\mathrm{when}\:\mathrm{x} \\ $$$$=\:\mathrm{0}\:,\mathrm{what}\:\mathrm{will}\:\mathrm{be}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\underset{\mathrm{t}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\underset{\mathrm{0}} {\overset{\mathrm{t}} {\int}}\:\mathrm{f}\left(\mathrm{x}\right)\:\mathrm{dx}}{\mathrm{t}^{\mathrm{2}} } \\ $$$$ \\ $$

Question Number 106214 Answers: 1 Comments: 0

solve : arc cos (x−1)= 2arc cos (x) where x is real.

$$\mathrm{solve}\::\:\mathrm{arc}\:\mathrm{cos}\:\left(\mathrm{x}−\mathrm{1}\right)=\:\mathrm{2arc}\:\mathrm{cos}\:\left(\mathrm{x}\right) \\ $$$$\mathrm{where}\:\mathrm{x}\:\mathrm{is}\:\mathrm{real}. \\ $$

Question Number 106220 Answers: 3 Comments: 0

find general solution cos (x−45°)=sin (2x+60°)

$$\mathrm{find}\:\mathrm{general}\:\mathrm{solution}\:\mathrm{cos}\:\left(\mathrm{x}−\mathrm{45}°\right)=\mathrm{sin}\:\left(\mathrm{2x}+\mathrm{60}°\right) \\ $$

Question Number 106196 Answers: 0 Comments: 5

Question Number 106188 Answers: 2 Comments: 0

Solve for x x^x^(...x^a ) =a with a∈R^+

$${Solve}\:{for}\:{x} \\ $$$${x}^{{x}^{...{x}^{{a}} } } ={a}\:{with}\:{a}\in\mathbb{R}^{+} \\ $$

Question Number 106238 Answers: 0 Comments: 0

Question Number 106239 Answers: 1 Comments: 0

A rope of length 10cm is used to form as ector of circle of radius 35cm What ish te size of the angle of the sector

$$ \\ $$$$\mathrm{A}\:\mathrm{rope}\:\mathrm{of}\:\mathrm{length}\:\mathrm{10cm}\:\mathrm{is}\:\mathrm{used}\:\mathrm{to}\:\mathrm{form}\:\mathrm{as} \\ $$$$\mathrm{ector}\:\mathrm{of}\:\mathrm{circle}\:\mathrm{of}\:\mathrm{radius}\:\mathrm{35cm}\:\mathrm{What}\:\mathrm{ish} \\ $$$$\mathrm{te}\:\mathrm{size}\:\mathrm{of}\:\mathrm{the}\:\mathrm{angle}\:\mathrm{of}\:\mathrm{the}\:\mathrm{sector} \\ $$

Question Number 106173 Answers: 2 Comments: 0

lim_(x→π/2) (((1−sin x)/(x^2 cot^2 x))) ?

$$\underset{{x}\rightarrow\pi/\mathrm{2}} {\mathrm{lim}}\left(\frac{\mathrm{1}−\mathrm{sin}\:\mathrm{x}}{\mathrm{x}^{\mathrm{2}} \mathrm{cot}\:^{\mathrm{2}} \mathrm{x}}\right)\:? \\ $$

Question Number 106167 Answers: 2 Comments: 0

Question Number 106163 Answers: 0 Comments: 0

Question Number 106175 Answers: 3 Comments: 0

lim_(x→0) (((√x)−(√(sin x)))/(x^2 (√x))) = ?

$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\sqrt{\mathrm{x}}−\sqrt{\mathrm{sin}\:\mathrm{x}}}{\mathrm{x}^{\mathrm{2}} \sqrt{\mathrm{x}}}\:=\:? \\ $$

Question Number 106161 Answers: 0 Comments: 2

If X=x+y−a+b Y=y+z×b Z=a^2 ×b^2 x=y=−1 a=b=4 then what is the answer of ((X+Y+Z)/(Y−Z)) ?

Question Number 106176 Answers: 3 Comments: 1

If 20 men can lay 36m of a pipe in 8 hours. How long would 25 men take to lay the next 54m of the pipe?

$$\mathrm{If}\:\mathrm{20}\:\mathrm{men}\:\mathrm{can}\:\mathrm{lay}\:\mathrm{36m}\:\mathrm{of}\:\mathrm{a}\:\mathrm{pipe} \\ $$$$\mathrm{in}\:\mathrm{8}\:\mathrm{hours}.\:\mathrm{How}\:\mathrm{long}\:\mathrm{would}\:\mathrm{25} \\ $$$$\mathrm{men}\:\mathrm{take}\:\mathrm{to}\:\mathrm{lay}\:\mathrm{the}\:\mathrm{next}\:\mathrm{54m}\:\mathrm{of} \\ $$$$\mathrm{the}\:\mathrm{pipe}? \\ $$

Question Number 106148 Answers: 2 Comments: 0

(1)∫ sec^(−1) x^2 dx (2) ∫(√(x+2)) sin^(−1) (√(3x−1)) dx

$$\left(\mathrm{1}\right)\int\:{sec}^{−\mathrm{1}} {x}^{\mathrm{2}} {dx} \\ $$$$ \\ $$$$\left(\mathrm{2}\right)\:\int\sqrt{{x}+\mathrm{2}}\:\:{sin}^{−\mathrm{1}} \sqrt{\mathrm{3}{x}−\mathrm{1}}\:{dx} \\ $$

Question Number 106152 Answers: 0 Comments: 0

lim_(x→0) ((1−cos xcos 2xcos 3x...cos nx)/x^n )

$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{1}−\mathrm{cos}\:\mathrm{xcos}\:\mathrm{2xcos}\:\mathrm{3x}...\mathrm{cos}\:\mathrm{nx}}{\mathrm{x}^{\mathrm{n}} } \\ $$

Question Number 106139 Answers: 0 Comments: 0

a,b∈Z ^3 (√(9^3 (√2) − 9)) = 1 −^3 (√a) +^3 (√b), a = ? b = ?

$${a},{b}\in\mathbb{Z}\:\:\:\:\:^{\mathrm{3}} \sqrt{\mathrm{9}\:^{\mathrm{3}} \sqrt{\mathrm{2}}\:−\:\mathrm{9}}\:=\:\mathrm{1}\:−\:^{\mathrm{3}} \sqrt{{a}}\:+\:^{\mathrm{3}} \sqrt{{b}},\:\:\:\:\:{a}\:=\:?\:\:\:\:\:\:{b}\:=\:? \\ $$

Question Number 106138 Answers: 1 Comments: 0

If root of equation x^3 −px^2 +qx−r=0 are in AP than what is the relation between p,q and r ?

$$\mathrm{If}\:\mathrm{root}\:\mathrm{of}\:\mathrm{equation}\:\mathrm{x}^{\mathrm{3}} −\mathrm{px}^{\mathrm{2}} +\mathrm{qx}−\mathrm{r}=\mathrm{0}\:\mathrm{are}\:\mathrm{in} \\ $$$$\mathrm{AP}\:\mathrm{than}\:\mathrm{what}\:\mathrm{is}\:\mathrm{the}\:\mathrm{relation}\:\mathrm{between}\:\mathrm{p},\mathrm{q} \\ $$$$\mathrm{and}\:\mathrm{r}\:? \\ $$

Question Number 106134 Answers: 0 Comments: 0

let g(x) =arcatan(1+x)ln(1−2x) 1) find g^((n)) (x) and g^((n)) (0) 2) developp f at integr serie 3/ calculate ∫_(−(1/4)) ^(1/4) g(x)dx

$$\mathrm{let}\:\mathrm{g}\left(\mathrm{x}\right)\:=\mathrm{arcatan}\left(\mathrm{1}+\mathrm{x}\right)\mathrm{ln}\left(\mathrm{1}−\mathrm{2x}\right) \\ $$$$\left.\mathrm{1}\right)\:\mathrm{find}\:\mathrm{g}^{\left(\mathrm{n}\right)} \left(\mathrm{x}\right)\:\mathrm{and}\:\mathrm{g}^{\left(\mathrm{n}\right)} \left(\mathrm{0}\right) \\ $$$$\left.\mathrm{2}\right)\:\mathrm{developp}\:\mathrm{f}\:\mathrm{at}\:\mathrm{integr}\:\mathrm{serie} \\ $$$$\mathrm{3}/\:\mathrm{calculate}\:\:\int_{−\frac{\mathrm{1}}{\mathrm{4}}} ^{\frac{\mathrm{1}}{\mathrm{4}}} \:\mathrm{g}\left(\mathrm{x}\right)\mathrm{dx} \\ $$

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