Exercises for Question Type 1: Maclaurin series with substitution

Question 1

Skill question

Find the Maclaurin expansion of $f (x) = 1 + 2 x$ up to and including the $x^{3}$ term.

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Question 2

Skill question

Obtain the Maclaurin series for $f (x) = arctan (2 x)$ up to and including the $x^{5}$ term.

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Question 3

Skill question

Determine the Maclaurin series for $f (x) = e^{5 x}$ up to and including the $x^{4}$ term.

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Question 4

Skill question

Determine the Maclaurin series of $f (x) = (1 + 2 x)^{- \frac{1}{2}}$ up to and including the $x^{3}$ term.

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Question 5

Skill question

Find the Maclaurin series for $f (x) = ln (1 + 2 x^{3})$ up to and including the $x^{9}$ term.

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Question 6

Skill question

Find the Maclaurin expansion of $f (x) = ln (1 - x^{2})$ up to and including the $x^{6}$ term.

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Question 7

Skill question

Find the Maclaurin series of $f (x) = \frac{1}{1 - x ^{2}}$ up to and including the $x^{6}$ term.

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Question 8

Skill question

Find the Maclaurin series expansion of $f (x) = arctan (3 x^{2})$ up to and including the $x^{6}$ term.

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Question 9

Skill question

Type: Long Answer | Level: - | Paper: -

Find the Maclaurin series for $f (x) = \frac{e ^{x} - 1}{x}$ up to and including the $x^{3}$ term.

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Question 10

Skill question

Determine the Maclaurin series for $f (x) = \frac{1}{1 + 3 x}$ up to and including the $x^{3}$ term.

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Question 11

Skill question

Type: Long Answer | Level: - | Paper: -

Find the Maclaurin series expansion of $f (x) = sin (4 x^{2})$ up to and including the $x^{6}$ term.

[3]

Question 12

Skill question

Obtain the Maclaurin series of $f (x) = ln (\frac{1 + x}{1 - x})$ up to and including the $x^{5}$ term.

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IB Mathematics Analysis and Approaches Question Type 1: Maclaurin Series with Substitution Exercises