Find the Limit of the Sequence If It Converges; Otherwise $$a _ { n } = \frac { 9 n - 3 } { 5 - 4 \sqrt { n } }$$

question 318

Multiple Choice

Find the limit of the sequence if it converges; otherwise indicate divergence.
- $$a _ { n } = \frac { 9 n - 3 } { 5 - 4 \sqrt { n } }$$

• A) \(\frac { 3 } { 4 }\)
• B) \(- \frac { 9 } { 4 }\)
• C) \(\frac { 9 } { 5 }\)
• D) Diverges

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Definitions:

Perfectly Competitive

A perfectly competitive market is characterized by many buyers and sellers, homogenous products, and free entry and exit, leading to price determination by market forces.

Marginal Cost Curve

A graphical representation that shows how the cost of producing one more unit of a good changes as the quantity produced increases.

Short-run Supply Curve

A graphical depiction that showcases how much of a product suppliers are willing and able to sell at different prices in the short run, with at least one input fixed.

Perfectly Competitive Industry

An industry characterized by many small firms producing identical products, with free entry and exit, and perfect information, leading to prices being determined by the market.