Find $\lim _ { h \rightarrow 0 } \frac { f ( x + h ) - f ( x ) } { h }$

question 214

Multiple Choice

Find $\lim _ { h \rightarrow 0 } \frac { f ( x + h ) - f ( x ) } { h }$ . $f ( x ) = \frac { 1 } { x - 3 }$

• A) \(\lim _ { h \rightarrow 0 } \frac { f ( x + h ) - f ( x ) } { h } = - \frac { 4 } { ( x - 3 ) ^ { - 2 } }\)
• B) \(\lim _ { h \rightarrow 0 } \frac { f ( x + h ) - f ( x ) } { h } = - \frac { 6 } { ( x - 3 ) ^ { 2 } }\)
• C) \(\lim _ { h \rightarrow 0 } \frac { f ( x + h ) - f ( x ) } { h } = - \frac { 1 } { ( x - 3 ) ^ { - 2 } }\)
• D) \(\lim _ { h \rightarrow 0 } \frac { f ( x + h ) - f ( x ) } { h } = \frac { 1 } { ( x - 3 ) ^ { 2 } }\)
• E) \(\lim _ { h \rightarrow 0 } \frac { f ( x + h ) - f ( x ) } { h } = - \frac { 1 } { ( x - 3 ) ^ { 2 } }\)

---

Definitions:

Rotation

The act or process of an object turning around an internal axis or center point.

Cupula

A gelatinous, dome-shaped structure in the vestibular system of the inner ear that contains hair cells and is pivotal in detecting head movements and maintaining balance.

Cochlear Nerve

The nerve that transmits auditory information from the cochlea in the inner ear to the brain.

Nystagmus

Involuntary, rapid, and repetitive movement of the eyes, which can be horizontal, vertical, or rotary, and may indicate underlying neurological problems.