Find the Limit $\lim _ { t \rightarrow 0 } \left[ \left( t ^ { 2 } + 3 \right) \mathbf { i } + \cos 5 t \mathbf { j } - 6 \mathbf { k } \right]$

question 70

Multiple Choice

Find the limit $\lim _ { t \rightarrow 0 } \left[ \left( t ^ { 2 } + 3 \right) \mathbf { i } + \cos 5 t \mathbf { j } - 6 \mathbf { k } \right]$ .

• A) \(3 \mathbf { i } - 6 \mathbf { k }\)
• B) \(4 \mathbf { i } + \mathbf { j }\)
• C) \(3 \mathbf { i } + \mathbf { j } - 6 \mathbf { k }\)
• D) \(4 i\)

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Definitions:

UV-visible Spectrum

A graphical representation of the absorption or emission of ultraviolet or visible radiation by a substance, used to characterize and analyze chemical substances.

Energy Absorption

The process by which a material takes in energy from its surroundings, often leading to physical or chemical changes.

(E)-1,3,5-hexatriene

A linear conjugated hydrocarbon with the formula C6H8, characterized by a specific geometric configuration (E) of its carbon-carbon double bonds.

Conjugated System

A chemical structure where alternating single and multiple bonds create a system of connected π-electrons, leading to unique stability and reactivity.