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Taylor series about a point practice problems

Taylor polynomials and series about a point other than 0. 10 problems with worked solutions; in 10 of them every equation is proved by a computer algebra system.

Find the Taylor polynomial of degree 3 for \( \displaystyle f(x) = \sqrt{x} \) centered at \( \displaystyle a = 4 \).

Problem 7.310medium✓ Nihil obstat

Find the Taylor polynomial of degree 3 for \( \displaystyle f(x) = \ln{\left(x \right)} \) centered at \( \displaystyle a = 1 \).

Problem 7.311medium✓ Every equation proved

Find the Taylor polynomial of degree 3 for \( \displaystyle f(x) = \cos{\left(x \right)} \) centered at \( \displaystyle a = \pi \).

Problem 7.314medium✓ Every equation proved

Find the Taylor polynomial of degree 3 for \( \displaystyle f(x) = \frac{1}{x} \) centered at \( \displaystyle a = 1 \).

Problem 7.315medium✓ Every equation proved

Find the Taylor polynomial of degree 3 for \( \displaystyle f(x) = x^{3} - 2 x \) centered at \( \displaystyle a = 1 \).

Problem 7.316medium✓ Every equation proved

Find the Taylor polynomial of degree 3 for \( \displaystyle f(x) = \sin{\left(x \right)} \) centered at \( \displaystyle a = \frac{\pi}{2} \).

Problem 7.317medium✓ Nihil obstat

Find the Taylor polynomial of degree 3 for \( \displaystyle f(x) = \frac{1}{x} \) centered at \( \displaystyle a = 2 \).

Problem 7.318medium✓ Every equation proved

Find the Taylor polynomial of degree 3 for \( \displaystyle f(x) = e^{x} \) centered at \( \displaystyle a = 1 \).

Problem 7.309hard✓ Every equation proved

Find the Taylor polynomial of degree 3 for \( \displaystyle f(x) = e^{x} \) centered at \( \displaystyle a = -1 \).

Problem 7.312hard✓ Every equation proved

Find the Taylor polynomial of degree 3 for \( \displaystyle f(x) = \ln{\left(x \right)} \) centered at \( \displaystyle a = 2 \).

Problem 7.313hard✓ Every equation proved