## University Calculus: Early Transcendentals (3rd Edition)

$|\space Error| \lt 1.25 \times 10^{-5}$
The Binomial series for $\sqrt{1+x}$ can be defined as: $\sqrt{1+x}=1+\dfrac{x}{2}-\dfrac{x^2}{8}+\dfrac{x^3}{16}-.....$ By the Alternating Series Estimation Theorem, the error can be calculated as: $|Error| \lt |\dfrac{-x^2}{8}|$ or, $|Error| \lt \dfrac{(0.01)^2}{8}$ or, $|\space Error| \lt 1.25 \times 10^{-5}$