Evaluate the Limit Given Below A) $36 \mathbf { i } + \mathbf { j } + \frac { 9 } { 4 } \mathbf { k }$

question 46

Multiple Choice

Evaluate the limit given below. $$\lim _ { t \rightarrow 4 } \left( 9 t \mathbf { i } + \frac { t ^ { 2 } - 16 } { t ^ { 2 } - 4 t } \mathbf { j } + \frac { 9 } { t } \mathbf { k } \right)$$

• A) \(36 \mathbf { i } + \mathbf { j } + \frac { 9 } { 4 } \mathbf { k }\)
• B) \(36 \mathbf { i } + 2 \mathbf { j } + \frac { 9 } { 4 } \mathbf { k }\)
• C) \(9 \mathbf { i } + 16 \mathbf { j } + \frac { 9 } { 4 } \mathbf { k }\)
• D) \(36 \mathbf { i } + \frac { 9 } { 4 } \mathbf { k }\)
• E) The limit does not exist.

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Definitions:

Transactions Exposure

Short-run financial risk arising from the need to buy or sell at uncertain prices or rates in the near future.

Financial Risk

The possibility of losing money on an investment or business venture; it can arise from various sources like market volatility, credit risk, or operational failures.

Uncertain Prices

Refers to the unpredictability in the cost of goods, services, or assets, often due to factors like market volatility, supply and demand imbalances, or economic uncertainties.

Near Future

A term referring to the time period that is just ahead, typically implying events or developments expected to occur within a short timeframe from the present.