Express the Limit as a Definite Integral $\lim_{{||P \| \rightarrow 0}} \sum_{k=1}^{n} \frac{7}{4-8 c_{k}^{2}} \Delta x_{k}$

question 16

Multiple Choice

Express the limit as a definite integral.

- $\lim_{{||P \| \rightarrow 0}} \sum_{k=1}^{n} \frac{7}{4-8 c_{k}^{2}} \Delta x_{k}$ , where $\mathrm { P }$ is a partition of $[ 10,12 ]$

• A) \(\int _ { 1 } ^ { n } \frac { 7 } { 4 - 8 x } d x\)
• B) \(\int _ { 12 } ^ { 10 } \frac { 7 } { 4 - 8 x ^ { 2 } } d x\)
• C) \(\int _ { 10 } ^ { 12 } \frac { 7 } { 4 - 8 x } d x\)
• D) \(\int _ { 10 } ^ { 12 } \frac { 7 } { 4 - 8 x ^ { 2 } } d x\)

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Definitions:

Promoter Region

A region of DNA that initiates transcription of a particular gene, essential for gene expression regulation.

Peptide Bond Formation

A biochemical process that involves the joining of two amino acids through a covalent bond between the amino group of one and the carboxyl group of the other, releasing a molecule of water.

tRNA

Transfer RNA; a type of RNA molecule that helps decode a messenger RNA (mRNA) sequence into a protein during the process of translation in protein synthesis.

Ribosome

Molecular machines within cells that synthesize proteins by translating the information contained in messenger RNA.