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

question 418

Multiple Choice

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

• A) \(f ( x ) \approx \frac { 1 } { \sqrt { 5 } } \left( 1 - \frac { x } { 2 \sqrt { 5 } } \right)\)
• B) \(f ( x ) \approx \sqrt { 5 } \left( 1 - \frac { x } { 10 } \right)\)
• C) \(f ( x ) \approx 5 - \frac { x } { 2 }\)
• D) \(f ( x ) \approx \frac { 1 } { \sqrt { 5 } } \left( 1 - \frac { x } { 10 } \right)\)

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