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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)) ?

$$\boldsymbol{\mathrm{If}}\: \\ $$$$\boldsymbol{\mathrm{X}}=\boldsymbol{\mathrm{x}}+\boldsymbol{\mathrm{y}}−\boldsymbol{\mathrm{a}}+\boldsymbol{\mathrm{b}} \\ $$$$\boldsymbol{\mathrm{Y}}=\boldsymbol{\mathrm{y}}+\boldsymbol{\mathrm{z}}×\boldsymbol{\mathrm{b}} \\ $$$$\boldsymbol{\mathrm{Z}}=\boldsymbol{\mathrm{a}}^{\mathrm{2}} ×\boldsymbol{\mathrm{b}}^{\mathrm{2}} \\ $$$$\boldsymbol{\mathrm{x}}=\boldsymbol{\mathrm{y}}=−\mathrm{1} \\ $$$$\boldsymbol{\mathrm{a}}=\boldsymbol{\mathrm{b}}=\mathrm{4} \\ $$$$\boldsymbol{\mathrm{then}}\:\boldsymbol{\mathrm{what}}\:\boldsymbol{\mathrm{is}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{answer}}\:\boldsymbol{\mathrm{of}}\: \\ $$$$\frac{\boldsymbol{\mathrm{X}}+\boldsymbol{\mathrm{Y}}+\boldsymbol{\mathrm{Z}}}{\boldsymbol{\mathrm{Y}}−\boldsymbol{\mathrm{Z}}}\:?\: \\ $$

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

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

Question Number 106133 Answers: 1 Comments: 0

let f(x) =e^(−2x) ln(3−x^2 ) 1) calculate f^((n)) (x)and f^((n)) (0) 2) developp f at integr serie

$$\mathrm{let}\:\mathrm{f}\left(\mathrm{x}\right)\:=\mathrm{e}^{−\mathrm{2x}} \mathrm{ln}\left(\mathrm{3}−\mathrm{x}^{\mathrm{2}} \right) \\ $$$$\left.\mathrm{1}\right)\:\mathrm{calculate}\:\mathrm{f}^{\left(\mathrm{n}\right)} \left(\mathrm{x}\right)\mathrm{and}\:\mathrm{f}^{\left(\mathrm{n}\right)} \left(\mathrm{0}\right) \\ $$$$\left.\mathrm{2}\right)\:\mathrm{developp}\:\mathrm{f}\:\mathrm{at}\:\mathrm{integr}\:\mathrm{serie} \\ $$

Question Number 106132 Answers: 0 Comments: 0

find ∫_(−∞) ^(+∞) x^2 e^(−x^2 ) ln(1+x^2 )dx

$$\mathrm{find}\:\int_{−\infty} ^{+\infty} \:\mathrm{x}^{\mathrm{2}} \mathrm{e}^{−\mathrm{x}^{\mathrm{2}} } \:\mathrm{ln}\left(\mathrm{1}+\mathrm{x}^{\mathrm{2}} \right)\mathrm{dx} \\ $$$$ \\ $$

Question Number 106123 Answers: 0 Comments: 2

In a △ABC with sides a=6cm,b=? and c=? area is 270cm^2 .And if midline of the △ is 7 cm find the value of sides b and c. Please solve this with a little explanation.

$${In}\:{a}\:\bigtriangleup{ABC}\:{with}\:{sides}\:\boldsymbol{{a}}=\mathrm{6}{cm},\boldsymbol{{b}}=?\:{and}\:\boldsymbol{{c}}=? \\ $$$${area}\:{is}\:\mathrm{270}{cm}^{\mathrm{2}} .{And}\:{if}\: \\ $$$${midline}\:{of}\:{the}\:\bigtriangleup\:{is}\:\mathrm{7}\:{cm} \\ $$$${find}\:{the}\:{value}\:{of}\:{sides}\:\:\boldsymbol{{b}}\:\boldsymbol{{and}}\:\boldsymbol{{c}}. \\ $$$$ \\ $$$$\boldsymbol{{Please}}\:\boldsymbol{{solve}}\:\boldsymbol{{this}}\:\boldsymbol{{with}}\:\boldsymbol{{a}}\:\boldsymbol{{little}} \\ $$$$\boldsymbol{{explanation}}. \\ $$

Question Number 106118 Answers: 1 Comments: 1

Question Number 106125 Answers: 2 Comments: 0

∫_(π/4) ^π (√(1−sin2x)) dx

$$\int_{\frac{\pi}{\mathrm{4}}} ^{\pi} \sqrt{\mathrm{1}−\mathrm{sin2}{x}}\:\mathrm{d}{x} \\ $$

Question Number 106156 Answers: 2 Comments: 1

Given { (((√(xy)) +(1/(√x)) +(1/(√y)) =9)),(((√x)+(√y) = 20)) :} where x > y. find the value of x(√y) −y(√x) .

$$\mathrm{Given}\:\begin{cases}{\sqrt{\mathrm{xy}}\:+\frac{\mathrm{1}}{\sqrt{\mathrm{x}}}\:+\frac{\mathrm{1}}{\sqrt{\mathrm{y}}}\:=\mathrm{9}}\\{\sqrt{\mathrm{x}}+\sqrt{\mathrm{y}}\:=\:\mathrm{20}}\end{cases} \\ $$$$\mathrm{where}\:\mathrm{x}\:>\:\mathrm{y}.\:\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of} \\ $$$$\mathrm{x}\sqrt{\mathrm{y}}\:−\mathrm{y}\sqrt{\mathrm{x}}\:. \\ $$

Question Number 106120 Answers: 1 Comments: 3

question 106075 again ∫((1+cosx)/((99cosx−70sinx+210)cosx−66sinx+110))dx=? using t=tan(x/2) I get −4∫(dt/(t^4 +8t^3 −22t^2 +272t−419)) can someone factorize the denominator?

$${question}\:\mathrm{106075}\:{again} \\ $$$$\int\frac{\mathrm{1}+{cosx}}{\left(\mathrm{99}{cosx}−\mathrm{70}{sinx}+\mathrm{210}\right){cosx}−\mathrm{66}{sinx}+\mathrm{110}}{dx}=? \\ $$$${using}\:{t}={tan}\left({x}/\mathrm{2}\right)\:{I}\:{get} \\ $$$$−\mathrm{4}\int\frac{{dt}}{{t}^{\mathrm{4}} +\mathrm{8}{t}^{\mathrm{3}} −\mathrm{22}{t}^{\mathrm{2}} +\mathrm{272}{t}−\mathrm{419}} \\ $$$${can}\:{someone}\:{factorize}\:{the}\:{denominator}? \\ $$

Question Number 106098 Answers: 1 Comments: 0

∫_(1/(2014)) ^(2014) ((tan^(−1) x)/x) dx

$$\int_{\frac{\mathrm{1}}{\mathrm{2014}}} ^{\mathrm{2014}} \frac{\mathrm{tan}^{−\mathrm{1}} {x}}{{x}}\:{dx} \\ $$

Question Number 106101 Answers: 1 Comments: 0

Question Number 106094 Answers: 0 Comments: 6

Question Number 106077 Answers: 0 Comments: 0

Given Σ_(n = 0) ^∞ cos^(2n) (θ) = 5. find the value of cos 2θ+cos 4θ+cos 8θ+cos 16θ+cos 32θ+...= (a) (1/5) (b) (3/5) (c) 2 (d) 1 (e) 3

$$\mathcal{G}\mathrm{iven}\:\underset{\mathrm{n}\:=\:\mathrm{0}} {\overset{\infty} {\sum}}\mathrm{cos}\:^{\mathrm{2n}} \left(\theta\right)\:=\:\mathrm{5}.\:\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of} \\ $$$$\mathrm{cos}\:\mathrm{2}\theta+\mathrm{cos}\:\mathrm{4}\theta+\mathrm{cos}\:\mathrm{8}\theta+\mathrm{cos}\:\mathrm{16}\theta+\mathrm{cos} \\ $$$$\mathrm{32}\theta+...= \\ $$$$\left(\mathrm{a}\right)\:\frac{\mathrm{1}}{\mathrm{5}}\:\:\:\:\:\left(\mathrm{b}\right)\:\frac{\mathrm{3}}{\mathrm{5}}\:\:\:\:\:\left(\mathrm{c}\right)\:\mathrm{2}\:\:\:\:\:\:\left(\mathrm{d}\right)\:\mathrm{1}\:\:\:\:\:\:\left(\mathrm{e}\right)\:\mathrm{3} \\ $$

Question Number 106076 Answers: 2 Comments: 0

solve this pls x^x^(1/2) =(1/2)

$${solve}\:{this}\:{pls} \\ $$$${x}^{{x}^{\frac{\mathrm{1}}{\mathrm{2}}} } =\frac{\mathrm{1}}{\mathrm{2}} \\ $$

Question Number 106075 Answers: 1 Comments: 0

∫((1+cosx)/((99cosx−70sinx+210)cosx−66sinx+110))dx=?

$$\int\frac{\mathrm{1}+{cosx}}{\left(\mathrm{99}{cosx}−\mathrm{70}{sinx}+\mathrm{210}\right){cosx}−\mathrm{66}{sinx}+\mathrm{110}}{dx}=? \\ $$

Question Number 106072 Answers: 2 Comments: 0

Question Number 106070 Answers: 0 Comments: 0

Question Number 106065 Answers: 0 Comments: 0

x^2 (d^2 y/dx^2 ) −x (dy/dx) +y = x

$$\mathrm{x}^{\mathrm{2}} \:\frac{\mathrm{d}^{\mathrm{2}} \mathrm{y}}{\mathrm{dx}^{\mathrm{2}} }\:−\mathrm{x}\:\frac{\mathrm{dy}}{\mathrm{dx}}\:+\mathrm{y}\:=\:\mathrm{x}\: \\ $$

Question Number 106044 Answers: 1 Comments: 0

Given f(x)=2x+m, f^(2 ) (x)=px+6 Find the value of m and p.

$$\mathrm{Given}\:\mathrm{f}\left(\mathrm{x}\right)=\mathrm{2x}+\mathrm{m},\:\mathrm{f}^{\mathrm{2}\:} \left(\mathrm{x}\right)=\mathrm{px}+\mathrm{6} \\ $$$$\mathrm{Find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{m}\:\mathrm{and}\:\mathrm{p}. \\ $$

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