Answer
$0.741$
Work Step by Step
$P_{4}(x) = \ln 2 + \frac{1}{2}(x-2) - \frac{1}{4 \times 2!}(x-2)^{2} + \frac{1}{4 \times 3!}(x-2)^{3} + \frac{3}{8 \times 4!} (x-2)^{4}$
$P_{4}(2.1)$, so replace $x$ with $2.1$
$P_{4}(2.1) = \ln 2 + \frac{1}{2}(2.1-2) - \frac{1}{4 \times 2!}(2.1-2)^{2} + \frac{1}{4 \times 3!}(2.1-2)^{3} + \frac{3}{8 \times 4!} (2.1-2)^{4}$
$P_{4}(2.1) = \ln 2 + \frac{1}{2}(0.1) - \frac{1}{8}(0.1)^{2} + \frac{1}{24}(0.1)^{3} + \frac{3}{64} (0.1)^{4}$
$P_{4}(2.1) = 0.741$
