Because of Their Connection with Secant Lines, Tangents, and Instantaneous $\lim _ { h \rightarrow 0 } \frac { f ( x + h ) - f ( x ) } { h }$

question 136

Multiple Choice

Because of their connection with secant lines, tangents, and instantaneous rates, limits of the form $\lim _ { h \rightarrow 0 } \frac { f ( x + h ) - f ( x ) } { h }$ occur frequently in calculus. Evaluate this limit for the given value of $x$ and function $f$ .
- $$( x ) = \frac { 2 } { x } , x = - 5$$

• A) 10
• B) \(- \frac { 2 } { 25 }\)
• C) Does not exist
• D) \(- \frac { 2 } { 5 }\)

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