Question Number 225003 by Tinku Tara last updated on 15/Oct/25

$$\mathrm{The}\:\mathrm{new}\:\mathrm{symbols}\:\mathrm{are}\:\mathrm{in} \\ $$$$\mathrm{progress}.\:\mathrm{New}\:\mathrm{update}\:\mathrm{will}\:\mathrm{be}\:\mathrm{release} \\ $$$$\mathrm{by}\:\mathrm{end}\:\mathrm{of}\:\mathrm{this}\:\mathrm{month}\:\mathrm{with} \\ $$$$-\:\mathrm{Close}\:\mathrm{integration}\:\mathrm{symbols} \\ $$$$-\:\mathrm{Italic}\:\mathrm{greek}\:\mathrm{capital}\:\mathrm{letters} \\ $$$$-\:\mathrm{Ability}\:\mathrm{to}\:\mathrm{upload}\:\mathrm{GIF}\:\mathrm{images} \\ $$$$ \\ $$$$\mathrm{If}\:\mathrm{anyone}\:\mathrm{has}\:\mathrm{any}\:\mathrm{other}\:\mathrm{improvement} \\ $$$$\mathrm{suggestion}\:\mathrm{please}\:\mathrm{email}\:\mathrm{us}\:\mathrm{or}\:\mathrm{comment} \\ $$$$\mathrm{here} \\ $$
Commented by mr W last updated on 15/Oct/25

$${also}\:{animated}\:{gif}\:{images}? \\ $$
Commented by Tawa11 last updated on 15/Oct/25

$$\boldsymbol{\mathrm{Conjugate}}\:\boldsymbol{\mathrm{symbol}}. \\ $$
Commented by fantastic last updated on 15/Oct/25
![please add nabla [▽] water image of Δ](https://www.tinkutara.com/question/Q225006.png)
$${please}\:{add}\:{nabla}\:\left[\bigtriangledown\right] \\ $$$${water}\:{image}\:{of}\:\Delta \\ $$
Commented by Tawa11 last updated on 15/Oct/25

Commented by Tawa11 last updated on 15/Oct/25

Commented by Tawa11 last updated on 15/Oct/25

$$\mathrm{And}\:\mathrm{ability}\:\mathrm{to}\:\mathrm{put}\:\mathrm{that}\:\:\mathrm{bar}\:\:\mathrm{and}\:\mathrm{the}\:\mathrm{subscript}\:\:\mathrm{k} \\ $$$$\mathrm{and}\:\mathrm{that}\:\mathrm{bracket}\:\mathrm{on}\:\:\:\mathrm{H} \\ $$
Commented by fantastic last updated on 15/Oct/25

$${and}\:{in}\:{the}\:{last}\:{row}\: \\ $$$${in}\:{the}\:''\:\mathrm{sin}''\:{button}\:{please}\:{add} \\ $$$$\frac{{dy}}{{dx}}\:{and}\:\frac{\partial{y}}{\partial{x}}\:{so}\:{we}\:{dont}\:{have}\:{to} \\ $$$${type}\:{it}\:{mannually} \\ $$
Commented by Tinku Tara last updated on 15/Oct/25
Yes. The GIF upload support is for animated GIF support request that you raised sometime back
Commented by fantastic last updated on 15/Oct/25

Commented by BaliramKumar last updated on 15/Oct/25

Commented by BaliramKumar last updated on 15/Oct/25

$$\mathrm{multyple}\:\mathrm{line}\:\mathrm{select}\:\mathrm{copy}\:\mathrm{and}\:\mathrm{paste}\:\mathrm{ability} \\ $$
Commented by Mathswiz last updated on 16/Oct/25
Sir
here are my suggetions:
1. The integration symbol should become larger if the expression gets bigger. Currently it remains small.
2. multiple lines select, copy, paste, font change, bold, italics, colour at one go
3. Introduce fonts like Times New Roman, Ariel, bold fonts for heading etc...
4. facility to convert to latex in math mode. Currently everything is converted in text mode using mathrm string
5. copy and paste of borderless tables creates borders which is not desired. For that we have charts with borders as another option
Commented by fantastic last updated on 16/Oct/25

$${you}\:{wake}\:{up}\:{early}. \\ $$$$\left.{good}\:{habit}\:…\::\right) \\ $$
Commented by fantastic last updated on 16/Oct/25

$${mirror}\:{ima}\:{ge} \\ $$
Commented by Tinku Tara last updated on 16/Oct/25

$$\mathrm{Latex}\:\mathrm{coversion} \\ $$$${f}\left({x}\right)={x}^{\mathrm{2}} \:\Rightarrow\:{math}\:{mode} \\ $$$$\mathrm{f}\left(\mathrm{x}\right)=\mathrm{x}^{\mathrm{2}} \:\:\:\Rightarrow\:\mathrm{mathrm} \\ $$
Commented by Tinku Tara last updated on 16/Oct/25
Converted Latex
$$\mathrm{Latex}\:\mathrm{coversion} \\ $$
$${f}\left({x}\right)={x}^{\mathrm{2}} \:\Rightarrow\:{math}\:{mode} \\ $$
$$\mathrm{f}\left(\mathrm{x}\right)=\mathrm{x}^{\mathrm{2}} \:\:\:\Rightarrow\:\mathrm{mathrm} \\ $$
Commented by fantastic last updated on 18/Oct/25
$$ \\ $$
$${I}\:{DO}\:{NOT}\:{KNOW}\:{IF}\:{MY}\:{WORK}\:{IS}\:{CORRECT} \\ $$
$${At}\:{first}\:{we}\:{are}\:{going}\:{ti}\:{find}\:{the}\:{distant}\:{s} \\ $$
$$\ell_{\mathrm{0}} −{R}\theta−{Rd}\theta=\ell_{\mathrm{0}} −{R}\theta\left[\theta\:{is}\:{tooooo}\:{small}\right] \\ $$
$${so}\:{ds}=\left(\ell_{\mathrm{0}} −{R}\theta\right){d}\theta \\ $$
$$\therefore{s}=\underset{\mathrm{0}} {\overset{\psi} {\int}}\left(\ell_{\mathrm{0}} −{R}\theta\right){d}\theta \\ $$
$${now}\:{R}\psi=\ell_{\mathrm{0}} \\ $$
$${so}\:\psi=\frac{\ell_{\mathrm{0}} }{{R}} \\ $$
$${so} \\ $$
$${s}=\overset{\ell_{\mathrm{0}} /{R}} {\int}_{\mathrm{0}} \left(\ell_{\mathrm{0}} −{R}\theta\right){d}\theta \\ $$
$$=\left[\ell_{\mathrm{0}} \theta−{R}\frac{\theta^{\mathrm{2}} }{\mathrm{2}}\right]_{\mathrm{0}} ^{\frac{\ell_{\mathrm{0}} }{{R}}} \\ $$
$$=\frac{\ell_{\mathrm{0}} ^{\mathrm{2}} }{{R}}−\frac{\ell_{\mathrm{0}} ^{\mathrm{2}} }{\mathrm{2}{R}} \\ $$
$$=\frac{\ell_{\mathrm{0}} ^{\mathrm{2}} }{\mathrm{2}{R}} \\ $$
$${So}\:{s}=\frac{\ell_{\mathrm{0}} ^{\mathrm{2}} }{\mathrm{2}{R}} \\ $$
$${now}\:{only}\:{kinetic}\:{friction}\:{will}\:{work}\:{here} \\ $$
$${v}_{{final}} =\mathrm{0} \\ $$
$${s}=\frac{\ell_{\mathrm{0}} ^{\mathrm{2}} }{\mathrm{2}{R}} \\ $$
$${u}={v}_{\mathrm{0}} \\ $$
$${a}_{{r}} =\frac{{mg}\mu_{{k}} }{{m}}={g}\mu_{{k}} \\ $$
$$\left({v}_{{final}} \right)^{\mathrm{2}} ={v}_{\mathrm{0}} ^{\mathrm{2}} −\mathrm{2}{as} \\ $$
$$\Rightarrow{v}_{\mathrm{0}} =\ell_{\mathrm{0}} \sqrt{\frac{{g}\mu_{{k}} }{{R}}} \\ $$
Answered by Kademi last updated on 19/Oct/25
![f′(x) → f ′(x) C^k → C^( k) ((x/y))^′ → ((x/y))^([′]) g^](https://www.tinkutara.com/question/Q225074.png)