Find $\lim _ { x \rightarrow 5 } [ g ( x ) - f ( x ) ]$

question 146

Multiple Choice

Find $\lim _ { x \rightarrow 5 } [ g ( x ) - f ( x ) ]$ for $f ( x ) = 5 x ^ { 3 }$ and $g ( x ) = \frac { \sqrt { x ^ { 2 } + 9 } } { 3 x ^ { 2 } }$ .

• A) \(\frac { \sqrt { 34 } } { 75 } - 625\)
• B) \(\frac { \sqrt { 34 } } { 75 } + 625\)
• C) \(\frac { \sqrt { 34 } } { 75 }\)
• D)limit does not exist
• E) \(\frac { 1 } { 75 } - 625\)

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Definitions:

Single-gene Disorder

A genetic condition caused by mutations in a single gene.

Gene Duplication

The process by which a segment of genetic material or a chromosome is duplicated or copied within the genome, leading to gene redundancy and potentially novel functions.

Gene Sequence

The order of nucleotides in a section of DNA or RNA that represents a fragment of the genetic code.