【webwork】 Chapter 3.10 solutions.－Josephood7

Jun 24 Fri 2022 16:54
【webwork】 Chapter 3.10 solutions.

Find a linear approximation of the function $f (x) = \sqrt[3]{1 + x}$ at $a = 0$ , and use it to approximate the numbers $\sqrt[3]{.98}$ and $\sqrt[3]{1.09}$ .

$\sqrt[3]{1 + x} \approx$
$\sqrt[3]{.98} \approx$
$\sqrt[3]{1.09} \approx$

The radius of a circular disk is given as 23 cm with a maximal error in measurement of 0.4 cm. Use differentials to estimate the following.

(a) The maximum error in the calculated area of the disk.
(b) The relative maximum error.
(c) The percentage error in that case.

Use differentials (or equivalently, a linear approximation) to approximate $\sin (26^{\circ})$ as follows: Let $f (x) = \sin (x)$ and find the equation of the tangent line to $f (x)$ at a "nice" point near $26^{\circ}$ . Then use this to approximate $\sin (26^{\circ})$ .