$$\text { Use the linear approximation } ( 1 + x ) ^ { k } \approx 1 + k x \text {, as specified. }$$
-Find an approximation for the function $f ( x ) = ( 1 - x ) ^ { 5 }$ for values of $x$ near zero.
A) $f ( x ) \approx 1 + 6 x$
B) $f ( x ) \approx 1 + 5 x$
C) $f ( x ) \approx 5 + 5 x$
D) $f ( x ) \approx 1 - 5 x$

Question

Quizplus · Accepted Answer

The linear approximation formula is $ ( 1 + x ) ^ { k } \approx 1 + k x $. For $f(x) = (1 - x)^5$, we can use $k = 5$ and $x$ replaced by $-x$, giving $f(x) \approx 1 - 5x$.

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.

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