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Question Number 103759 Answers: 3 Comments: 0

(x^5 +3y) dx −x dy = 0

$$\left({x}^{\mathrm{5}} +\mathrm{3}{y}\right)\:{dx}\:−{x}\:{dy}\:=\:\mathrm{0}\: \\ $$

Question Number 103796 Answers: 1 Comments: 2

Σ_(k = 1) ^n k^5 = ?

$$\underset{{k}\:=\:\mathrm{1}} {\overset{{n}} {\sum}}{k}^{\mathrm{5}} \:=\:? \\ $$

Question Number 103756 Answers: 1 Comments: 1

Question Number 103755 Answers: 0 Comments: 0

Π_(n = 3) ^∞ (1−tan^4 ((π/2^n ))) = ?

$$\underset{{n}\:=\:\mathrm{3}} {\overset{\infty} {\prod}}\left(\mathrm{1}−\mathrm{tan}\:^{\mathrm{4}} \left(\frac{\pi}{\mathrm{2}^{{n}} }\right)\right)\:=\:? \\ $$

Question Number 103753 Answers: 1 Comments: 0

→ { ((g(x)=(6/(x−2)))),(((goh)(3) = 17)),((h(x)= ax^2 −1)) :} find the value of a

$$\rightarrow\begin{cases}{{g}\left({x}\right)=\frac{\mathrm{6}}{{x}−\mathrm{2}}}\\{\left({goh}\right)\left(\mathrm{3}\right)\:=\:\mathrm{17}}\\{{h}\left({x}\right)=\:{ax}^{\mathrm{2}} −\mathrm{1}}\end{cases} \\ $$$${find}\:{the}\:{value}\:{of}\:{a}\: \\ $$

Question Number 103751 Answers: 1 Comments: 0

given that the parametric equation of a curvd are x=(1/(t−1)) y=(1/(t+1)) obtaun a cartesian equation of the curve. Hemce find an equqtion of tbe nirmal to the curve at the point t=2

$$ \\ $$$${given}\:{that}\:{the}\:{parametric}\:{equation}\:{of}\: \\ $$$${a}\:{curvd}\:{are}\:{x}=\frac{\mathrm{1}}{{t}−\mathrm{1}}\:\:{y}=\frac{\mathrm{1}}{{t}+\mathrm{1}}\:{obtaun}\:{a}\: \\ $$$${cartesian}\:{equation}\:{of}\:{the}\:{curve}.\:{Hemce}\:{find} \\ $$$${an}\:{equqtion}\:{of}\:{tbe}\:{nirmal}\:{to}\:{the}\:{curve}\:{at}\:{the}\: \\ $$$${point}\:{t}=\mathrm{2} \\ $$

Question Number 103749 Answers: 3 Comments: 0

lim_(n→∞) 2^n sin ((π/2^n )) = ?

$$\underset{{n}\rightarrow\infty} {\mathrm{lim}}\:\mathrm{2}^{{n}} \:\mathrm{sin}\:\left(\frac{\pi}{\mathrm{2}^{{n}} }\right)\:=\:? \\ $$

Question Number 103808 Answers: 0 Comments: 1

muhun kitu pisan

$${muhun}\:{kitu}\:{pisan} \\ $$

Question Number 103742 Answers: 1 Comments: 0

calculate ∫_0 ^∞ (dx/((2x+1)^4 (x+3)^5 ))

$$\mathrm{calculate}\:\int_{\mathrm{0}} ^{\infty} \:\:\:\:\frac{\mathrm{dx}}{\left(\mathrm{2x}+\mathrm{1}\right)^{\mathrm{4}} \left(\mathrm{x}+\mathrm{3}\right)^{\mathrm{5}} } \\ $$

Question Number 103741 Answers: 1 Comments: 0

calculate ∫_0 ^∞ ((arctan(ch(x)))/(x^2 +9))dx

$$\mathrm{calculate}\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{\mathrm{arctan}\left(\mathrm{ch}\left(\mathrm{x}\right)\right)}{\mathrm{x}^{\mathrm{2}} \:+\mathrm{9}}\mathrm{dx} \\ $$

Question Number 103739 Answers: 1 Comments: 0

Question Number 103738 Answers: 0 Comments: 2

Prime-counting function: π(x) What is the name of her reciprocal function? (Like arcsin(x) is the reciprocal function of sin(x)) [■ ■_(−) ^(−) ]

$$\mathrm{Prime}-\mathrm{counting}\:\mathrm{function}: \\ $$$$\pi\left({x}\right) \\ $$$$ \\ $$$$\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{name}\:\mathrm{of}\:\mathrm{her} \\ $$$$\mathrm{reciprocal}\:\mathrm{function}? \\ $$$$ \\ $$$$\left(\mathrm{Like}\:\mathrm{arcsin}\left({x}\right)\:\mathrm{is}\:\mathrm{the}\right. \\ $$$$\left.\mathrm{reciprocal}\:\mathrm{function}\:\mathrm{of}\:\mathrm{sin}\left({x}\right)\right) \\ $$$$ \\ $$$$\left[\underset{−} {\overline {\blacksquare\:\:\:\blacksquare}}\right] \\ $$

Question Number 103736 Answers: 0 Comments: 0

Solve: a^2 + c^2 = 196 ... (i) b^2 + (c − a)^2 = 169 ... (ii) c^2 + (b − c)^2 = 225 ... (iii)

$$\mathrm{Solve}:\:\:\:\:\:\:\mathrm{a}^{\mathrm{2}} \:\:+\:\:\mathrm{c}^{\mathrm{2}} \:\:=\:\:\:\mathrm{196}\:\:\:\:\:\:...\:\left(\mathrm{i}\right) \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{b}^{\mathrm{2}} \:\:+\:\:\left(\mathrm{c}\:\:−\:\:\mathrm{a}\right)^{\mathrm{2}} \:\:=\:\:\mathrm{169}\:\:\:\:\:...\:\left(\mathrm{ii}\right) \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{c}^{\mathrm{2}} \:\:+\:\:\left(\mathrm{b}\:\:−\:\:\mathrm{c}\right)^{\mathrm{2}} \:\:=\:\:\mathrm{225}\:\:\:\:\:...\:\left(\mathrm{iii}\right) \\ $$

Question Number 103723 Answers: 0 Comments: 0

Solve for n, such that; 1−(1/2)+∙∙∙+(((−1)^n )/(n+1))=∫_0 ^1 (x^(n+1) /(1+x))dx−ln2−(−1)^(n+1)

$$\mathrm{Solve}\:\mathrm{for}\:\mathrm{n},\:\mathrm{such}\:\mathrm{that}; \\ $$$$\mathrm{1}−\frac{\mathrm{1}}{\mathrm{2}}+\centerdot\centerdot\centerdot+\frac{\left(−\mathrm{1}\right)^{\mathrm{n}} }{\mathrm{n}+\mathrm{1}}=\int_{\mathrm{0}} ^{\mathrm{1}} \frac{\mathrm{x}^{\mathrm{n}+\mathrm{1}} }{\mathrm{1}+\mathrm{x}}\mathrm{dx}−\mathrm{ln2}−\left(−\mathrm{1}\right)^{\mathrm{n}+\mathrm{1}} \\ $$

Question Number 103716 Answers: 1 Comments: 3

Question Number 103703 Answers: 1 Comments: 0

if an object moves along a straight line according to the relationship( x(t)=((1/2)t^2 −t+2)) find (1) the average speed between (x=(3/2) , x=(7/2)) (2) the pelvic velocity between (x=(7/2))

$${if}\:{an}\:{object}\:{moves}\:{along}\:{a}\:{straight}\:{line}\: \\ $$$${according}\:{to}\:{the}\:{relationship}\left(\:{x}\left({t}\right)=\left(\frac{\mathrm{1}}{\mathrm{2}}{t}^{\mathrm{2}} −{t}+\mathrm{2}\right)\right) \\ $$$${find}\: \\ $$$$\left(\mathrm{1}\right)\:{the}\:{average}\:{speed}\:{between}\:\left({x}=\frac{\mathrm{3}}{\mathrm{2}}\:,\:{x}=\frac{\mathrm{7}}{\mathrm{2}}\right) \\ $$$$\left(\mathrm{2}\right)\:{the}\:{pelvic}\:{velocity}\:{between}\:\left({x}=\frac{\mathrm{7}}{\mathrm{2}}\right) \\ $$

Question Number 103700 Answers: 1 Comments: 1

Question Number 103691 Answers: 1 Comments: 0

solve for x x^x =s

$${solve}\:{for}\:{x} \\ $$$${x}^{{x}} ={s} \\ $$

Question Number 103686 Answers: 1 Comments: 0

x^x^6 =(√2)^(√2) x=?

$${x}^{{x}^{\mathrm{6}} } =\sqrt{\mathrm{2}}\:^{\sqrt{\mathrm{2}}} \:{x}=? \\ $$

Question Number 103685 Answers: 1 Comments: 0

Question Number 103683 Answers: 1 Comments: 1

∫_0 ^1 tan^(−1) (((2x−1)/(1+x−x^2 )))dx

$$\int_{\mathrm{0}} ^{\mathrm{1}} {tan}^{−\mathrm{1}} \left(\frac{\mathrm{2}{x}−\mathrm{1}}{\mathrm{1}+{x}−{x}^{\mathrm{2}} }\right){dx} \\ $$

Question Number 103673 Answers: 1 Comments: 0

Σ_(k=1) ^(4095) (1/(((√k)+(√(k+1)))((k)^(1/4) +((k+1))^(1/4) ))) ?

$$\underset{{k}=\mathrm{1}} {\overset{\mathrm{4095}} {\sum}}\frac{\mathrm{1}}{\left(\sqrt{{k}}+\sqrt{{k}+\mathrm{1}}\right)\left(\sqrt[{\mathrm{4}}]{{k}}+\sqrt[{\mathrm{4}}]{{k}+\mathrm{1}}\right)}\:? \\ $$

Question Number 103672 Answers: 1 Comments: 3

Question Number 103670 Answers: 4 Comments: 0

Given b_n = 3.2^n is a GP . find the value of (1/b_1 )+(1/b_2 )+(1/b_3 )+...+(1/b_(10) ) ?

$${Given}\:{b}_{{n}} \:=\:\mathrm{3}.\mathrm{2}^{{n}} \:{is}\:{a}\:{GP}\:.\:{find}\:{the}\:{value} \\ $$$${of}\:\frac{\mathrm{1}}{{b}_{\mathrm{1}} }+\frac{\mathrm{1}}{{b}_{\mathrm{2}} }+\frac{\mathrm{1}}{{b}_{\mathrm{3}} }+...+\frac{\mathrm{1}}{{b}_{\mathrm{10}} }\:?\: \\ $$

Question Number 103669 Answers: 2 Comments: 0

prove that : a) ∫_(−3) ^(−1) x^2 dx ≥∫_1 ^3 (2x−1)dx b)∫_(−2) ^0 xdx ≤∫_0 ^2 (x^2 + x )dx c)∫_1 ^4 (x^2 + 2)dx ≥∫_2 ^5 (2x −5)dx d)∫_(−π) ^(−((3π)/4)) cos 2x dx ≥∫_((3π)/4) ^π sin 2x dx

$${prove}\:{that}\:: \\ $$$$\left.{a}\right)\:\int_{−\mathrm{3}} ^{−\mathrm{1}} {x}^{\mathrm{2}} {dx}\:\geqslant\int_{\mathrm{1}} ^{\mathrm{3}} \left(\mathrm{2}{x}−\mathrm{1}\right){dx} \\ $$$$\left.{b}\right)\int_{−\mathrm{2}} ^{\mathrm{0}} {xdx}\:\leqslant\int_{\mathrm{0}} ^{\mathrm{2}} \left({x}^{\mathrm{2}} \:+\:{x}\:\right){dx} \\ $$$$\left.{c}\right)\int_{\mathrm{1}} ^{\mathrm{4}} \left({x}^{\mathrm{2}} \:+\:\mathrm{2}\right){dx}\:\:\geqslant\int_{\mathrm{2}} ^{\mathrm{5}} \left(\mathrm{2}{x}\:−\mathrm{5}\right){dx} \\ $$$$\left.{d}\right)\int_{−\pi} ^{−\frac{\mathrm{3}\pi}{\mathrm{4}}} \mathrm{cos}\:\mathrm{2}{x}\:{dx}\:\geqslant\int_{\frac{\mathrm{3}\pi}{\mathrm{4}}} ^{\pi} \mathrm{sin}\:\mathrm{2}{x}\:{dx} \\ $$$$ \\ $$$$ \\ $$$$ \\ $$

Question Number 103665 Answers: 0 Comments: 0

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