Find Each of the Following Limits or Explain Why It $\lim _ { x \rightarrow 0 } \frac { x - \sin x } { x ^ { 3 } }$

question 172

Essay

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

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Definitions:

Working Capital

This refers to the amount by which current assets exceed current liabilities, indicating the liquidity available to a business for day-to-day operations.

Current Liabilities

Short-term financial obligations that are due within one year or within the normal operating cycle of a business.

Current Assets

Resources anticipated to be transformed into cash, sold, or utilized within a year or during the standard operational cycle of the company.

Fiscal Year

A one-year period that companies and governments use for accounting purposes and preparing financial statements, which may not align with the calendar year.