End-of-chapter review exercise 21: check 1
Difficulty: ★★☆Maths4U Original · Short practice
The curve \(x^2+1y^2=365\) passes through \((13,14)\).
Find 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.
End-of-chapter review exercise 21: review variant 1
Difficulty: ★★☆Maths4U Original · Short practice
The curve \(x^2+2y^2=646\) passes through \((14,15)\).
Find 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.
End-of-chapter review exercise 21: check 2
Difficulty: ★★☆Maths4U Original · Short practice
The curve \(x^2+2y^2=646\) passes through \((14,15)\).
Find d²y/dx² at the point.
Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.
End-of-chapter review exercise 21: review variant 2
Difficulty: ★★☆Maths4U Original · Short practice
The curve \(x^2+3y^2=993\) passes through \((15,16)\).
Find d²y/dx² at the point.
Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.
End-of-chapter review exercise 21: check 3
Difficulty: ★★☆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.
End-of-chapter review exercise 21: review variant 3
Difficulty: ★★☆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.
End-of-chapter review exercise 21: check 4
Difficulty: ★★☆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.
End-of-chapter review exercise 21: review variant 4
Difficulty: ★★☆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 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.