Use Differentials to Approximate the Arc Length of the Graph $\mathbf { P }$

question 35

Short Answer

Use differentials to approximate the arc length of the graph of the equation from $\mathbf { P }$ to $\mathbf { Q }$ . Round answer to four decimal places.
$$y = x ^ { 3 } + 3 ; \mathrm { P } ( 1,4 ) , \quad \mathrm { Q } ( 1.2,4.728 )$$

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Definitions:

Carbon Bonds

Refers to the covalent bonding between carbon atoms or between carbon and other atoms, forming a variety of organic and inorganic compounds.

Carbon Bonds

The chemical bonds between carbon atoms or between carbon and other atoms which constitute the backbone of organic compounds.

Organic Structures

Three-dimensional arrangements of atoms within an organic molecule, determining its chemical behavior and interactions.

End-Carbon Atoms

The carbon atoms located at the extremities of a carbon chain in organic molecules, often involved in reactions due to their unique positions.