Determine the Third Taylor Polynomial of F(x) = Ln(2 - $\ln ( 1.3 ) .$

question 99

Short Answer

Determine the third Taylor polynomial of f(x) = ln(2 - x) at x = 1 and use it to estimate $\ln ( 1.3 ) .$ [Hint: $\ln ( 1.3 ) = f ( 0.7 )$ .]
Enter your answer as an unlabeled polynomial in $x - 1$ in standard form : $\ln ( 1.3 ) \approx p _ { 3 } ( 0.7 ) = 0.264$

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Definitions:

Partial Correlation

A numerical index that reflects the relationship between two variables with the removal of the influence of a third variable (called a mediating or confounding variable).

Absolute Value

A numerical value without regard to its sign, often represented as the distance of a number from zero on the real number line.

One-tailed

A one-tailed test in statistics is a hypothesis test where the region of rejection is on only one side of the sampling distribution, focusing on a direction of interest.

Two-tailed

A statistical test that considers both directions for the possibility of a relationship in the population, not just one or the other.