Chapter 6 Multiple choice questions

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. Which of the following is not true about a Taylor series?

It is a polynomial approximation. correct incorrect

It is most accurate in the vicinity of a chosen point. correct incorrect

It is a special case of a Maclaurin series. correct incorrect

It should not be used outside its radius of convergence. correct incorrect

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. Which of the following is not true about a Maclaurin series?

The series for cos(x) can be derived from the series for sin(x). correct incorrect

The series for ln(1+x) converges for all x. correct incorrect

The series for e^x converges for all x. correct incorrect

The binomial expansion is a Taylor series. correct incorrect

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. What does tan(x) / x tend towards in the limit that x goes to 0?

0 correct incorrect

1 correct incorrect

It diverges to infinity. correct incorrect

None of the above. correct incorrect

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. How does y = x e^-x - sin(x) behave in the region around x=0?

y ≈ -x² correct incorrect

y ≈-x correct incorrect

y ≈ x correct incorrect

y ≈ x² correct incorrect

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. What does ln(x) / (1-x) tend towards in the limit that x goes to 1?

It diverges to infinity. correct incorrect

0 correct incorrect

-1 correct incorrect

None of the above. correct incorrect