Question and Answers Forum

AllQuestion and Answers: Page 1822

Question Number 28159 Answers: 0 Comments: 1

let give D=[0,(π/2)]×[0,(1/2)] find the value of ∫∫_D ((dxdy)/(ycosx +1)) .

$${let}\:{give}\:{D}=\left[\mathrm{0},\frac{\pi}{\mathrm{2}}\right]×\left[\mathrm{0},\frac{\mathrm{1}}{\mathrm{2}}\right]\:\:{find}\:{the}\:{value}\:{of} \\ $$$$\int\int_{{D}} \:\:\:\frac{{dxdy}}{{ycosx}\:+\mathrm{1}}\:\:. \\ $$

Question Number 28158 Answers: 1 Comments: 0

calculate ∫∫_(x^2 +y^2 ≤1) ((dxdy)/(3+x^2 +y^2 )) .

$${calculate}\:\int\int_{{x}^{\mathrm{2}} +{y}^{\mathrm{2}} \leqslant\mathrm{1}} \:\:\:\frac{{dxdy}}{\mathrm{3}+{x}^{\mathrm{2}} +{y}^{\mathrm{2}} }\:\:. \\ $$

Question Number 28185 Answers: 1 Comments: 0

M, N are endpoints of a diameter 4x−y=15 of circle x^2 +y^2 −6x+6y−16=0 ; and are also on the tangents at the end points of the major axis of an ellipse respectively, such that MN is also tangent to the same ellipse at point P. If the major axis of the ellipse is along y=x, find eccentricity, length of latus rectum, centre and equation of derectrices.

$${M},\:{N}\:{are}\:{endpoints}\:{of}\:{a}\:{diameter} \\ $$$$\:\mathrm{4}{x}−{y}=\mathrm{15}\:\:{of}\:{circle} \\ $$$${x}^{\mathrm{2}} +{y}^{\mathrm{2}} −\mathrm{6}{x}+\mathrm{6}{y}−\mathrm{16}=\mathrm{0}\:;\:{and}\:{are} \\ $$$${also}\:{on}\:{the}\:{tangents}\:{at}\:{the}\:{end} \\ $$$${points}\:{of}\:{the}\:{major}\:{axis}\:{of}\:{an} \\ $$$${ellipse}\:{respectively},\:{such}\:{that} \\ $$$${MN}\:{is}\:{also}\:{tangent}\:{to}\:{the}\:{same} \\ $$$${ellipse}\:{at}\:{point}\:{P}. \\ $$$${If}\:{the}\:{major}\:{axis}\:{of}\:{the}\:{ellipse} \\ $$$${is}\:{along}\:{y}={x},\:{find} \\ $$$$\:\:\:{eccentricity},\:{length}\:{of}\:{latus} \\ $$$${rectum},\:{centre}\:{and}\:{equation}\:{of} \\ $$$${derectrices}. \\ $$

Question Number 28151 Answers: 0 Comments: 4

lim_(x→1) ((1/(log_e x)) − (x/(x − 1)))

$$\underset{{x}\rightarrow\mathrm{1}} {\mathrm{lim}}\:\:\left(\frac{\mathrm{1}}{\mathrm{log}_{\mathrm{e}} \mathrm{x}}\:−\:\frac{\mathrm{x}}{\mathrm{x}\:−\:\mathrm{1}}\right) \\ $$

Question Number 28139 Answers: 1 Comments: 0

Question Number 28138 Answers: 0 Comments: 1

studie and?give the graph for the function f(x)= e^x −x^e .

$${studie}\:{and}?{give}\:{the}\:{graph}\:{for}\:{the}\:{function} \\ $$$${f}\left({x}\right)=\:{e}^{{x}} \:\:−{x}^{{e}} \:\:\:\:\:. \\ $$

Question Number 28202 Answers: 1 Comments: 1

Question Number 28201 Answers: 0 Comments: 0

prove the sine rule using dot product need help please

$$\mathrm{prove}\:\mathrm{the}\:\mathrm{sine}\:\mathrm{rule}\:\mathrm{using}\:\mathrm{dot}\:\mathrm{product} \\ $$$$\mathrm{need}\:\mathrm{help}\:\mathrm{please} \\ $$

Question Number 28143 Answers: 1 Comments: 0

x−(1/x)=3 x^2 −(1/x^2 )=?

$$\mathrm{x}−\frac{\mathrm{1}}{\mathrm{x}}=\mathrm{3} \\ $$$$\mathrm{x}^{\mathrm{2}} −\frac{\mathrm{1}}{\mathrm{x}^{\mathrm{2}} }=? \\ $$

Question Number 28124 Answers: 0 Comments: 3

f(R^+ →R) is a differentiable function obeying 2f(x)=f(xy)+f((x/y)) for all x,y ∈ R^+ and f(1)=0, f ′(1)=1 . Find f(x). More questions may follow..

$${f}\left({R}^{+} \rightarrow{R}\right)\:{is}\:{a}\:{differentiable} \\ $$$${function}\:{obeying} \\ $$$$\mathrm{2}{f}\left({x}\right)={f}\left({xy}\right)+{f}\left(\frac{{x}}{{y}}\right) \\ $$$${for}\:{all}\:{x},{y}\:\in\:{R}^{+} \:{and}\: \\ $$$${f}\left(\mathrm{1}\right)=\mathrm{0},\:{f}\:'\left(\mathrm{1}\right)=\mathrm{1}\:. \\ $$$${Find}\:{f}\left({x}\right).\:{More}\:{questions}\:{may} \\ $$$${follow}.. \\ $$

Question Number 28116 Answers: 0 Comments: 0

Question Number 28105 Answers: 0 Comments: 1

Question Number 28098 Answers: 1 Comments: 0

lim_(x→∞) ((log_e x)/x^h ) , h > 0

$$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\:\frac{\mathrm{log}_{\mathrm{e}} \mathrm{x}}{\mathrm{x}^{\mathrm{h}} }\:,\:\:\:\:\:\:\:\:\:\:\:\mathrm{h}\:>\:\mathrm{0} \\ $$

Question Number 28097 Answers: 0 Comments: 3

lim_(x→∞) ((3^x − 2^x )/x^2 )

$$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\:\frac{\mathrm{3}^{\mathrm{x}} \:−\:\mathrm{2}^{\mathrm{x}} }{\mathrm{x}^{\mathrm{2}} } \\ $$

Question Number 28096 Answers: 0 Comments: 2

lim_(x→∞) (x^2 /(x − sinx))

$$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\:\frac{\mathrm{x}^{\mathrm{2}} }{\mathrm{x}\:−\:\mathrm{sinx}} \\ $$

Question Number 28095 Answers: 0 Comments: 2

lim_(x→0^− ) (1 + tanx)^(−cotx)

$$\underset{{x}\rightarrow\mathrm{0}^{−} } {\mathrm{lim}}\:\:\left(\mathrm{1}\:+\:\mathrm{tanx}\right)^{−\mathrm{cotx}} \\ $$

Question Number 28093 Answers: 0 Comments: 2

lim_(x→0^− ) (1 + tanx)^(cotx)

$$\underset{{x}\rightarrow\mathrm{0}^{−} } {\mathrm{lim}}\:\:\left(\mathrm{1}\:+\:\mathrm{tanx}\right)^{\mathrm{cotx}} \\ $$

Question Number 28113 Answers: 1 Comments: 1

Question Number 28110 Answers: 0 Comments: 1

Question Number 28088 Answers: 0 Comments: 6

lim_(x→0^+ ) (sinx)^((tanx))

$$\underset{{x}\rightarrow\mathrm{0}^{+} } {\mathrm{lim}}\:\:\left(\mathrm{sinx}\right)^{\left(\mathrm{tanx}\right)} \\ $$

Question Number 28084 Answers: 0 Comments: 6

lim_(x→∞) (x − log_e x)

$$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\:\left(\mathrm{x}\:−\:\mathrm{log}_{\mathrm{e}} \mathrm{x}\right) \\ $$

Question Number 28076 Answers: 1 Comments: 1

Question Number 28075 Answers: 0 Comments: 0

Question Number 28073 Answers: 0 Comments: 1

find ∫_0 ^1 e^(−2x) ln(1+t e^(−x) )dx with 0<t<1 .

$${find}\:\:\int_{\mathrm{0}} ^{\mathrm{1}} \:{e}^{−\mathrm{2}{x}} {ln}\left(\mathrm{1}+{t}\:{e}^{−{x}} \right){dx}\:\:\:{with}\:\:\mathrm{0}<{t}<\mathrm{1}\:\:. \\ $$

Question Number 28072 Answers: 0 Comments: 1

let give the function f(x)=x^4 2π periodic and even developp f atfourier series.

$${let}\:{give}\:{the}\:{function}\:\:{f}\left({x}\right)={x}^{\mathrm{4}} \:\:\:\mathrm{2}\pi\:{periodic}\:{and}\:{even} \\ $$$${developp}\:\:\:{f}\:{atfourier}\:{series}. \\ $$

Question Number 28071 Answers: 0 Comments: 3

let give A_p = ∫_0 ^π t^p cos(nx) with nand p from N 1) find a relation between A_p and A_(p−2) 2) find arelation between A_(2p) and A_(2p−2) 3) find a relation?betweer A_(2p+1) and A_(2p−1) 3) cslculat A_(0 ) , A_1 , A_2 , A_2 .

$${let}\:{give}\:\:{A}_{{p}} =\:\int_{\mathrm{0}} ^{\pi} \:{t}^{{p}} \:{cos}\left({nx}\right)\:\:{with}\:{nand}\:{p}\:{from}\:{N} \\ $$$$\left.\mathrm{1}\right)\:{find}\:{a}\:{relation}\:{between}\:\:{A}_{{p}} \:{and}\:{A}_{{p}−\mathrm{2}} \\ $$$$\left.\mathrm{2}\right)\:{find}\:{arelation}\:{between}\:\:{A}_{\mathrm{2}{p}} \:\:{and}\:{A}_{\mathrm{2}{p}−\mathrm{2}} \\ $$$$\left.\mathrm{3}\right)\:{find}\:{a}\:{relation}?{betweer}\:{A}_{\mathrm{2}{p}+\mathrm{1}} \:{and}\:\:{A}_{\mathrm{2}{p}−\mathrm{1}} \\ $$$$\left.\mathrm{3}\right)\:{cslculat}\:\:{A}_{\mathrm{0}\:} ,\:{A}_{\mathrm{1}} ,\:{A}_{\mathrm{2}} \:,\:{A}_{\mathrm{2}} . \\ $$

Pg 1817 Pg 1818 Pg 1819 Pg 1820 Pg 1821 Pg 1822 Pg 1823 Pg 1824 Pg 1825 Pg 1826

Contact: info@tinkutara.com