Maclaurin series · Short practice

Check a final answer, then explain the reasoning on paper. Guest progress stays in this browser; an account saves future checks without overwriting your first result.

Recall

Maclaurin expansions — objective 1

Maths4U Original · Short practice

Let \(f(x)=e^{4 x} \cos{\left(3 x \right)}\). Write \(f(x)=1+Ax+Bx^2+Cx^3+O(x^4)\).

Find A.

Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.

Fresh review variant

Maclaurin expansions — objective 1

Maths4U Original · Short practice

Let \(f(x)=e^{x} \cos{\left(x \right)}\). Write \(f(x)=1+Ax+Bx^2+Cx^3+O(x^4)\).

Find A.

Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.

Method

Maclaurin expansions — objective 2

Maths4U Original · Short practice

Let \(f(x)=e^{x} \cos{\left(x \right)}\). Write \(f(x)=1+Ax+Bx^2+Cx^3+O(x^4)\).

Find B.

Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.

Fresh review variant

Maclaurin expansions — objective 2

Maths4U Original · Short practice

Let \(f(x)=e^{4 x} \cos{\left(x \right)}\). Write \(f(x)=1+Ax+Bx^2+Cx^3+O(x^4)\).

Find B.

Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.

Apply

Maclaurin expansions — objective 3

Maths4U Original · Short practice

Let \(f(x)=e^{2 x} \cos{\left(2 x \right)}\). Write \(f(x)=1+Ax+Bx^2+Cx^3+O(x^4)\).

Find C.

Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.

Fresh review variant

Maclaurin expansions — objective 3

Maths4U Original · Short practice

Let \(f(x)=e^{3 x} \cos{\left(3 x \right)}\). Write \(f(x)=1+Ax+Bx^2+Cx^3+O(x^4)\).

Find C.

Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.

Check understanding

Maclaurin expansions — objective 4

Maths4U Original · Short practice

Let \(f(x)=e^{3 x} \cos{\left(3 x \right)}\). Write \(f(x)=1+Ax+Bx^2+Cx^3+O(x^4)\).

Use the cubic polynomial to approximate f(\frac{3}{50}).

Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.

Fresh review variant

Maclaurin expansions — objective 4

Maths4U Original · Short practice

Let \(f(x)=e^{4 x} \cos{\left(x \right)}\). Write \(f(x)=1+Ax+Bx^2+Cx^3+O(x^4)\).

Use the cubic polynomial to approximate f(\frac{1}{50}).

Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.

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