Show That F Is Conservative and Find a Function F $\mathbf { F } = \nabla f$

question 55

Multiple Choice

Show that F is conservative and find a function f such that $\mathbf { F } = \nabla f$ , and use this result to evaluate $\int _ { C } \mathbf { F } \cdot d \mathbf { r }$ , where C is any path from $A \left( x _ { 0 } , y _ { 0 } \right)$ to $B \left( x _ { 1 } , y _ { 1 } \right)$ . $\mathbf { F } ( x , y ) = \left( 4 x y ^ { 2 } - 10 x y ^ { 2 } \right) \mathbf { i } + \left( 4 x ^ { 2 } y - 10 x ^ { 2 } y \right) \mathbf { j }$ ; $A ( 3,0 )$ and $B ( 3,2 )$

• A) \(\int _ { C } \mathbf { F } \cdot d \mathbf { r } = - 80\)
• B) \(\int _ { C } \mathbf { F } \cdot d \mathbf { r } = - 164\)
• C) \(\int _ { C } \mathbf { F } \cdot d \mathbf { r } = - 108\)
• D) \(\int _ { C } \mathbf { F } \cdot d \mathbf { r } = - 342\)

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Definitions:

Shares

units of ownership interest in a corporation or financial asset, providing a portion of the profits to shareholders as dividends.

Goodwill Impairment

The process of evaluating and adjusting the carrying value of goodwill on the balance sheet when it exceeds the fair market value, indicating that the acquired asset is not as valuable as originally thought.

IFRS

International Financial Reporting Standards, a set of accounting standards developed by the International Accounting Standards Board (IASB) that serve as a global framework for financial reporting.

ASPE

Accounting Standards for Private Enterprises, which provide simplified accounting guidelines for private companies in Canada.