Question Number 171136 by pablo1234523 last updated on 08/Jun/22 | ||
$$\mathrm{Using}\:\mathrm{Taylor}'\mathrm{s}\:\mathrm{theorem},\:\mathrm{prove}\:\mathrm{that} \\ $$ $${x}−\frac{{x}^{\mathrm{3}} }{\mathrm{6}}<\mathrm{sin}\:{x}<{x}−\frac{{x}^{\mathrm{3}} }{\mathrm{6}}+\frac{{x}^{\mathrm{5}} }{\mathrm{120}}\:\:\:\mathrm{for}\:{x}>\mathrm{0} \\ $$ | ||
Commented bypablo1234523 last updated on 08/Jun/22 | ||
Commented bypablo1234523 last updated on 08/Jun/22 | ||
$$\uparrow\:\mathrm{example} \\ $$ | ||
Commented bypablo1234523 last updated on 08/Jun/22 | ||
Commented bypablo1234523 last updated on 08/Jun/22 | ||
$$\theta{x}>\mathrm{0} \\ $$ $$\mathrm{what}\:\mathrm{does}\:\mathrm{it}\:\mathrm{imply}\:\mathrm{about}\:\mathrm{cos}\:\left(\theta{x}\right)? \\ $$ | ||