$$\text { Use the linear approximation } ( 1 + x ) ^ { k } \approx 1 + k x \text {, as specified. }$$
-$$\text { Estimate } \sqrt [ 3 ] { 1.012 }$$
A) 1.05
B) 1.004
C) 1.005
D) 1.04

Question

Quizplus · Accepted Answer

The linear approximation formula for $(1 + x)^k \approx 1 + kx$ can be used to estimate $\sqrt[3]{1.012}$ by setting $k = \frac{1}{3}$ and $x = 0.012$, resulting in $1 + \frac{1}{3}(0.012) = 1.004$.

Use the linear approximation (1+x)k≈1+kx, as specified. \text { Use the linear approximation } ( 1 + x ) ^ { k } \approx 1 + k x \text {, as specified. } Use the linear approximation (1+x)k≈1+kx, as specified.

$\text { Use the linear approximation } ( 1 + x ) ^ { k } \approx 1 + k x \text {, as specified. }$