Use the Derivative of the Taylor Series About 0 For \frac{1}{1-x}

question 4

Multiple Choice

Use the derivative of the Taylor series about 0 for $\frac{1}{1-x}$ to find the Taylor series about 0 for $\frac{4 x}{(1-x) ^{2}}$ .

• A) \(4+4 x^{3}+4 x^{5}+4 x^{7}+\cdots\)
• B) \(4+4 x^{2}+4 x^{3}+4 x^{4}+\cdots\)
• C) \(4 x+8 x^{2}+12 x^{3}+16 x^{4}+\cdots\)
• D) \(4+8 x+12 x^{2}+16 x^{3}+\cdots\)

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Definitions:

Confirmation Error

A cognitive bias that involves favoring information that confirms previously existing beliefs or biases.

Framing Error

A mistake in decision-making caused by misrepresenting or misinterpreting the context or information surrounding the decision.

Escalating Commitment

The phenomenon of individuals or organizations continuing to invest in a decision, project, or course of action despite evidence of its failure.

Anchoring Bias

A cognitive bias where an individual depends too heavily on an initial piece of information (the "anchor") when making decisions.