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

question 282

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 $f$ .
- $$f ( x ) = \sqrt { x } , x = 13$$

• A) Does not exist
• B) \(\frac { \sqrt { 13 } } { 13 }\)
• C) \(\frac { 13 } { 2 }\)
• D) \(\frac { \sqrt { 13 } } { 26 }\)

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Definitions:

Grapheme-Colour Synesthesia

A condition where an individual's perception of numbers and letters is associated with the experience of colors.

Dyslexia

A learning disorder characterized by difficulty in reading due to problems identifying speech sounds and learning how they relate to letters and words.

Emotional Synesthesia

A condition where emotional experiences trigger sensory perceptions in other domains, like seeing colors when feeling emotions.

Just Noticeable Difference

The smallest change in the intensity of a stimulus required to produce a detectable difference in the sensory perception.