Find Each of the Following Limits or Explain Why It $\lim _ { x \rightarrow 1 } \frac { x ^ { 3 } - 3 x + 2 } { 1 - x }$

question 33

Essay

Find each of the following limits or explain why it does not exist.(a) $\lim _ { x \rightarrow 1 } \frac { x ^ { 3 } - 3 x + 2 } { 1 - x }$ (b) $\lim _ { x \rightarrow 0 ^ { + } } \frac { \cos x - 1 } { x ^ { 2 } }$ (c) $\lim _ { x \rightarrow 0 ^ { + } } x ^ { 2 } ( \ln x )$

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Definitions:

Externalities

Effects of a transaction that affect third parties who did not choose to be involved in the market transaction, which can be either positive or negative.

Nonrivalry

A characteristic of a good where one person's consumption does not diminish the ability of others to consume the same good.

Public Good

A commodity or service that is provided without profit to all members of a society, either by the government or a private individual or organization.

Voluntarily Pay

Refers to making a payment or contribution freely without coercion, typically in contexts where payments are not legally mandated.