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

question 183

Multiple Choice

Find $\lim _ { x \rightarrow 5 } [ g ( x ) - f ( x ) ]$ for $f ( x ) = 3 x ^ { 3 } \text { and } g ( x ) = \frac { \sqrt { x ^ { 2 } + 6 } } { 6 x ^ { 2 } }$ .

• A) \(\frac { \sqrt { 31 } } { 150 } - 375\)
• B) \(\frac { \sqrt { 31 } } { 150 } + 375\)
• C) \(\frac { 1 } { 150 } - 375\)
• D) \(\frac { \sqrt { 31 } } { 375 } - 150\)
• E)limit does not exist

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Definitions:

Straight-Line Method

A method of calculating depreciation by evenly allocating the cost of an asset minus its salvage value over its estimated useful life.

Office Furniture

Items and fixtures used in an office setting for the purpose of work, including desks, chairs, and file cabinets.

Revised Annual Depreciation

The updated calculation of depreciation expense per year after making any necessary adjustments to asset value or useful life.

Depreciable Cost

The expense of a fixed asset reduced by its salvage value, indicating the entire sum that can be depreciated throughout the asset's lifespan.