End-of-chapter review exercise 21 · 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

Implicit first and second derivatives — objective 1

Maths4U Original · Short practice

The curve \(x^2+1y^2=365\) passes through \((13,14)\).

Find \(\displaystyle \frac{dy}{dx}\) at the point.

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

Fresh review variant

Implicit first and second derivatives — objective 1

Maths4U Original · Short practice

The curve \(x^2+2y^2=646\) passes through \((14,15)\).

Find \(\displaystyle \frac{dy}{dx}\) at the point.

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

Method

Implicit first and second derivatives — objective 2

Maths4U Original · Short practice

The curve \(x^2+2y^2=646\) passes through \((14,15)\).

Find \(\displaystyle \frac{d^{2}y}{dx^{2}}\) at the point.

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

Fresh review variant

Implicit first and second derivatives — objective 2

Maths4U Original · Short practice

The curve \(x^2+3y^2=993\) passes through \((15,16)\).

Find \(\displaystyle \frac{d^{2}y}{dx^{2}}\) at the point.

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

Apply

Parametric first and second derivatives — objective 3

Maths4U Original · Short practice

\(x=t^2+16,\ y=t^3+3t\), for t>0. Evaluate the requested quantities at \(t=3\).

Find the tangent y-intercept.

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

Fresh review variant

Parametric first and second derivatives — objective 3

Maths4U Original · Short practice

\(x=t^2+17,\ y=t^3+4t\), for t>0. Evaluate the requested quantities at \(t=4\).

Find the tangent y-intercept.

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

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

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

Fresh review variant

Maclaurin expansions — objective 4

Maths4U Original · Short practice

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

Use the cubic polynomial to approximate \(\displaystyle f(\frac{1}{25})\).

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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