Using-Taylor-s-theorem-prove-that-x-x-3-6-lt-sin-x-lt-x-x-3-6-x-5-120-for-x-gt-0-

Question Number 171136 by pablo1234523 last updated on 08/Jun/22

Using Taylor′s theorem, prove that x−(x^3 /6)<sin x<x−(x^3 /6)+(x^5 /(120)) for x>0

$$\mathrm{Using}\:\mathrm{Taylor}'\mathrm{s}\:\mathrm{theorem},\:\mathrm{prove}\:\mathrm{that} \\ $$$${x}−\frac{{x}^{\mathrm{3}} }{\mathrm{6}}<\mathrm{sin}\:{x}<{x}−\frac{{x}^{\mathrm{3}} }{\mathrm{6}}+\frac{{x}^{\mathrm{5}} }{\mathrm{120}}\:\:\:\mathrm{for}\:{x}>\mathrm{0} \\ $$

Commented by pablo1234523 last updated on 08/Jun/22