For $f(x)=x^{2} e^{10 x}$ , Find a Function $F(x)$ Such That $F^{\prime}(x)=f(x)$ And $F(0)=0$

question 39

Multiple Choice

For $f(x) =x^{2} e^{10 x}$ , find a function $F(x)$ such that $F^{\prime}(x) =f(x)$ and $F(0) =0$ .

• A) \(e^{10 x}\left(\frac{1}{10} x^{2}-\frac{1}{50} x+\frac{1}{500}\right)-\frac{1}{500}\)
• B) \(e^{10 x}\left(\frac{1}{10} x^{2}-\frac{1}{50} x+\frac{1}{500}\right)\)
• C) \(e^{10 x}\left(\frac{1}{10} x^{2}-\frac{1}{50} x\right)\)
• D) \(e^{10 x}\left(\frac{x^{3}}{30}\right)\)

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Definitions:

Working Capital

The excess of the current assets of a business over its current liabilities.

Current Assets

Assets that are expected to be converted into cash, sold, or used up within one year or within the business's operating cycle.

Horizontal Analysis

A method used in financial analysis to compare historical financial information over a series of reporting periods.

Comparative Financial Statement

Financial statements that provide financial data for multiple periods, facilitating the analysis of trends over time.