Limit of tan(sin{(x)})sin(tan{(x))} when x approaches 0

Marquis Neal

Answered question

2022-01-26

Limit of $\frac{\mathrm{tan}\left(\mathrm{sin}\left\{\left(x\right)\right\}\right)}{\mathrm{sin}\left(\mathrm{tan}\left\{\left(x\right)\right)\right\}}$ when x approaches 0

Answer & Explanation

bekiffen32

Beginner2022-01-27Added 8 answers

HINT
By standard limits use that
$\frac{\mathrm{tan}\left(\mathrm{sin}\left\{x\right\}\right)}{\mathrm{sin}\left(\mathrm{tan}\left\{x\right\}\right)}=\frac{\mathrm{tan}\left(\mathrm{sin}\left\{x\right\}\right)}{\mathrm{sin}x}\frac{\mathrm{tan}x}{\mathrm{sin}\left(\mathrm{tan}\left\{x\right\}\right)}\frac{\mathrm{sin}x}{x}\frac{x}{\mathrm{tan}x}$