(A) Find the Third-Order Taylor Polynomial Associated With $f ( x ) = \sin ^ { - 1 } x \text { at } a = 0$

question 77

Essay

(a) Find the third-order Taylor polynomial associated with $f ( x ) = \sin ^ { - 1 } x \text { at } a = 0$ .(b) Use the Taylor polynomial from part (a) to find an approximation of $\sin ^ { - 1 } 0.2$ .(c) Compare the value you calculated in part (b) with your calculator's value for $\sin ^ { - 1 } 0.2$

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Definitions:

Break-Even Point

An output at which a firm makes a normal profit (total revenue = total cost) but not an economic profit.

Total Revenue

The total income received by a firm from selling its goods or services, calculated as the quantity sold multiplied by the selling price per unit.

Short-Run Supply Curve

A supply curve that shows the quantity of a product a firm in a purely competitive industry will offer to sell at various prices in the short run; the portion of the firm’s short-run marginal cost curve that lies above its average-variable-cost curve.

Marginal Cost Curve

A graph that shows the relationship between the marginal cost of producing an additional unit and the quantity of that unit produced.