$$\text { Use the linear approximation } ( 1 + x ) ^ { k } \approx 1 + k x \text {, as specified. }$$
-Find an approximation for the function $f ( x ) = \frac { 2 } { 1 - x }$ for values of $x$ near zero.
A) $f ( x ) \approx 2 + 2 x$
B) $f ( x ) \approx 1 + 2 x$
C) $f ( x ) \approx 1 - 2 x$
D) $f ( x ) \approx 2 - 2 x$

Question

Quizplus · Accepted Answer

The given function can be rewritten as $f(x) = 2(1 - x)^{-1}$. Using the linear approximation $(1 + x)^k \approx 1 + kx$, we can substitute $k = -1$ and $x$ with $-x$ to get $f(x) \approx 2(1 + (-1)(-x)) = 2 + 2x$.

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.

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