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Questions >> TN XII Math >> Differential Calculus Applications - II

Trace the curve $y$ = $x^{3}$ Discuss the following curves for extence,symmetry,Asymptotes and loops

answered Aug 19, 2013 by meena.p

1 answer

$y^{2}$ = $x^{2}(1-x)$

answered Aug 19, 2013 by meena.p

1 answer

Trace the curve : $y^{2}(2+x)=x^{2}(6-x)$

answered Aug 19, 2013 by meena.p

1 answer

Trace the curve: $y^{2}$ $=x^{2}(1-x^{2})$

answered Aug 19, 2013 by meena.p

1 answer

$y^{2}$ = $(x-a)(x-b)^{2};a,b>0,a>b,$

answered Aug 19, 2013 by meena.p

1 answer

If $u= e^{\large\frac{x}{y}}\sin\frac{x}{y}+e^{\large\frac{y}{x}}\cos\frac{y}{x},$ Show that $x\large\frac{\partial u}{\partial x}+y\frac{\partial u}{\partial y}=u$

answered Aug 13, 2013 by meena.p

1 answer

Using Euler's theorem prove the following: $\;u=xy^{2}\sin\large(\frac{x}{y}),$ show that $x\large\frac{\partial u}{\partial x}+$ $y=\large\frac{\partial u}{\partial y}=$ $3u.$

answered Aug 13, 2013 by meena.p

1 answer

Using Euler's theorem prove the following: if $\;u=\tan^{-1}\large[\frac{x^{3}+y^{3}}{x-y}]$ prove that $x\large\frac{\partial u}{\partial x}$ + $y\large\frac{\partial u}{\partial y}=$ $\sin 2u$

answered Aug 13, 2013 by meena.p

1 answer

Find $\large\frac{\partial w}{\partial u}$ and $\large\frac{\partial w}{\partial v}$ if $\;w=\sin^{-1}xy$ where $x=u+v,y=u-v$

answered Aug 13, 2013 by meena.p

1 answer

Find $\large\frac{\partial w}{\partial u}$ and $\large\frac{\partial w}{\partial v}$ if $\;w=x^{2}+y^{2}$ where $x=u^{2}-v^{2},y=2uv$

answered Aug 13, 2013 by meena.p

1 answer

Find $\large\frac{\partial w}{\partial r}$ and $\large\frac{\partial w}{\partial \theta}$ if $\;w=\log(x^{2}+y^{2})$ where $\;x=r\cos\theta,y=r\sin\theta$

answered Aug 13, 2013 by meena.p

1 answer

Using chain rule find $\large\frac{dw}{dt}$ for each of the following $\;w=xy+z$ where $x=\cos t,y=\sin t$

answered Aug 13, 2013 by meena.p

1 answer

Using chain rule find $\large\frac{dw}{dt}$ for each of the following: $\;w=\large(\frac{x}{x^{2}+y^{2}})$ where $x=\cos t,y=\sin t.$

answered Aug 13, 2013 by meena.p

1 answer

Using chain rule find $\large\frac{dw}{dt}$ for each of the following : $w=\log(x^{2}+y^{2})$ where $x=e^{t},y=e^{-t}$

answered Aug 13, 2013 by meena.p

1 answer

Using chain rule find $\large\frac{dw}{dt}$ for each of the following : $w=e^{xy}$ Where $x=t^{2},y=t^{3}$

answered Aug 13, 2013 by meena.p

1 answer

If $u=\sqrt{x^{2}+y^{2}},$ Show that $x\large\frac{\partial u}{\partial x}+y\frac{\partial u}{\partial y}=u$

answered Aug 13, 2013 by meena.p

1 answer

Varify $\large\frac{\partial^{2} y}{\partial x\partial y}=\frac{\partial^{2} y}{\partial y\partial x}$ for the following function; $\;u=\tan^{-1}\large(\frac{x}{y})$

answered Aug 12, 2013 by meena.p

1 answer

Verify $\large\frac{\partial ^{2} y}{\partial x\partial y}=\frac{\partial ^{2} y}{\partial y\partial x}$ for the following function; $\;u=\sin 3x\cos4y$

answered Aug 12, 2013 by meena.p

1 answer

Verify $\large\frac{\partial ^{2} y}{\partial x\partial y}=\frac{\partial ^{2} y}{\partial y\partial x}$ for the following function; $\;u=\large\frac{x}{y^{2}}-\frac{y}{x^{2}}$

answered Aug 12, 2013 by meena.p

1 answer

Verify $\large\frac{\partial ^{2} y}{\partial x\partial y}=\frac{\partial ^{2} y}{\partial y\partial x}$ for the following function; $\;u=x^{2}+3xy+y^{2}$

answered Aug 12, 2013 by meena.p

1 answer

The radius of a circular disc is given as $24cm$ with a maximum error in mesurement of $0.02cm$ compute the relative error?

answered Aug 12, 2013 by meena.p

1 answer

The radius of a circular disc is given as $24cm$ with a maximum error in mesurement of $0.02cm$ Use differentials to estimate the maximum error in the calculated area of the dise.

answered Aug 12, 2013 by meena.p

1 answer

The edge of a cube was found to be $30cm$ with a possible error in mesurement of $0.1cm$ . Use differentials to estimate the maximum possible error in computing the surfacearea of the cube .

answered Aug 12, 2013 by meena.p

1 answer

The edge of a cube was found to be $30cm$ with a possible error in mesurement of $0.1cm$ . Use differentials to estimate the maximum possible error in computing the volume of the cube .

answered Aug 12, 2013 by meena.p

1 answer

Use differentials to find an approximate value for the given numbers $(1.97)^{6}$

answered Aug 12, 2013 by meena.p

1 answer

Use differentials to find an approximate value for the given numbers $y=3\sqrt{1.02}+4\sqrt{1.02}$

answered Aug 12, 2013 by meena.p

1 answer

Use differentials to find an approximate value for the given numbers $\large\frac{1}{10.1}$

answered Aug 12, 2013 by meena.p

1 answer

Use differentials to find an approximate value for the given numbers $\sqrt{36.1}$

answered Aug 12, 2013 by meena.p

1 answer

Find the differential $dy$ and evaluate $dy$ for the given values of $x$ and $dx$ $y=\cos$ $x,x=\large\frac{\pi}{6},$ $dx=0.05$

answered Aug 12, 2013 by meena.p

1 answer

Find the differential $dy$ and evaluate $dy$ for the given values of $x$ and $dx$ $y=\sqrt{1-x},x=0,dx=0.02$

answered Aug 12, 2013 by meena.p

1 answer

Find the differential $dy$ and evaluate $dy$ for the given values of $x$ and $dx$ $y=(x^{2}+5)^{3},x=1,dx=0.1$

answered Aug 12, 2013 by meena.p

1 answer

Find the differential $dy$ and evaluate $dy$ for the given values of $x$ and $dx$ $y$ = $x^{4}-3x^{2}+x-1,x$ $=2,dx$ $=0.1$

answered Aug 12, 2013 by meena.p

1 answer

Find the differential $dy$ and evaluate $dy$ for the given values of $x$ and $dx$ $y$ $=1-x^{2},x$ $=5,dx$ $=\large\frac{1}{2}$

answered Aug 12, 2013 by meena.p

1 answer

Find the differential of the functions. $y$ = $x\tan$ $x$

answered Aug 12, 2013 by meena.p

1 answer

Find the differential of the functions. $y$ = $\sin$ $2x$

answered Aug 12, 2013 by meena.p

1 answer

Find the differential of the functions. $y$ = $\large\frac{x-2}{2x+3}$

answered Aug 12, 2013 by meena.p

1 answer

Find the differential of the functions. $y$ = $\sqrt{x^{4}+x^{2}+1}$

answered Aug 12, 2013 by meena.p

1 answer

Find the differential of the functions. $y$ = $4\sqrt{x}$

answered Aug 12, 2013 by meena.p

1 answer

Find the differential of the functions. $y$ $=x^{5}$

answered Aug 12, 2013 by meena.p

1 answer

Using Euler's theorem prove the following: if $\;V=x^{ax+by}$ and $\;z$ is a homogenous function of degree $\;n$ in $\;x$ and $\;y$ prove that $\;x=\large\frac{\partial v}{\partial x}$ + $y\large\frac{\partial v}{\partial y}$ = $(ax+by+n)V.$

asked Apr 26, 2013 by poojasapani_1

0 answers

Using Euler's theorem prove the following: if $u$ is a homogenous function of $x$ and $y$ of degree $\;n$ , prove that $\;x\large\frac{\partial^{2} u}{\partial x^{2}}$ + $y\large\frac{\partial^{2}u}{\partial x\partial y}$ = $(n-1)\large\frac{\partial u}{\partial x}$

asked Apr 26, 2013 by poojasapani_1

0 answers

If $\;u=e^{y}\sin y\frac{x}{y}+e^{y}\cos x \frac{y}{x},$ Show that $x\large\frac{\partial u}{\partial x}+y\frac{\partial u}{\partial y}=o$

asked Apr 25, 2013 by poojasapani_1

0 answers

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