# Math Help - Approximation using Taylor's Theorem

1. ## Approximation using Taylor's Theorem

If $x>0$ show that $|(1+x)^{1/3}-(1+\frac{1}{3}x-\frac{1}{9}x^2)|\leq (5/81)x^3$ .
Use this inequality to approximate $\sqrt[3]{1.2}$ and $\sqrt[3]{2}$ .

2. Originally Posted by Kipster1203
If $x>0$ show that $|(1+x)^{1/3}-(1+\frac{1}{3}x-\frac{1}{9}x^2)|\leq (5/81)x^3$ .
Use this inequality to approximate $\sqrt[3]{1.2}$ and $\sqrt[3]{2}$ .
Apply Taylor's formula and look at the remainder term. Report back if you have any issues.