Implicit differentiation and tangents: check 1
Difficulty: ★★☆Info
Maths4U Original · Short practice
The curve satisfies \(x^2+3xy+y^2=20\). Consider \(\displaystyle P=\)\(\left( 2, \ 2\right)\). For the short checks \(\displaystyle a=3\).
Find \(\displaystyle \frac{dy}{dx}\) at the stated point.
Enter one number or fraction. Keep exact values during your working; use at least six decimal places for an approximate final answer. A calculator may be used.
Implicit differentiation and tangents: review variant 1
Difficulty: ★★☆Info
Maths4U Original · Short practice
The curve satisfies \(x^2+3xy+y^2=76\). Consider \(\displaystyle P=\)\(\left( 6, \ 2\right)\). For the short checks \(\displaystyle a=3\).
Find \(\displaystyle \frac{dy}{dx}\) at the stated point.
Enter one number or fraction. Keep exact values during your working; use at least six decimal places for an approximate final answer. A calculator may be used.
Implicit differentiation and tangents: check 2
Difficulty: ★★☆Info
Maths4U Original · Short practice
The curve satisfies \(x^2+1xy+y^2=27\). Consider \(\displaystyle P=\)\(\left( 3, \ 3\right)\). For the short checks \(\displaystyle a=1\).
Find the tangent y-intercept there.
Enter one number or fraction. Keep exact values during your working; use at least six decimal places for an approximate final answer. A calculator may be used.
Implicit differentiation and tangents: review variant 2
Difficulty: ★★☆Info
Maths4U Original · Short practice
The curve satisfies \(x^2+3xy+y^2=80\). Consider \(\displaystyle P=\)\(\left( 4, \ 4\right)\). For the short checks \(\displaystyle a=3\).
Find the tangent y-intercept there.
Enter one number or fraction. Keep exact values during your working; use at least six decimal places for an approximate final answer. A calculator may be used.
Implicit differentiation and tangents: check 3
Difficulty: ★★☆Info
Maths4U Original · Short practice
The curve satisfies \(x^2+3xy+y^2=80\). Consider \(\displaystyle P=\)\(\left( 4, \ 4\right)\). For the short checks \(\displaystyle a=3\).
Find the normal gradient there.
Enter one number or fraction. Keep exact values during your working; use at least six decimal places for an approximate final answer. A calculator may be used.
Implicit differentiation and tangents: review variant 3
Difficulty: ★★☆Info
Maths4U Original · Short practice
The curve satisfies \(x^2+3xy+y^2=76\). Consider \(\displaystyle P=\)\(\left( 6, \ 2\right)\). For the short checks \(\displaystyle a=3\).
Find the normal gradient there.
Enter one number or fraction. Keep exact values during your working; use at least six decimal places for an approximate final answer. A calculator may be used.
Implicit differentiation and tangents: check 4
Difficulty: ★★☆Info
Maths4U Original · Short practice
The curve satisfies \(x^2+1xy+y^2=75\). Consider \(\displaystyle P=\)\(\left( 5, \ 5\right)\). For the short checks \(\displaystyle a=1\).
Find the value of \(\displaystyle x^{2}\)+axy+\(\displaystyle y^{2}\) at the stated point.
Enter one number or fraction. Keep exact values during your working; use at least six decimal places for an approximate final answer. A calculator may be used.
Implicit differentiation and tangents: review variant 4
Difficulty: ★★☆Info
Maths4U Original · Short practice
The curve satisfies \(x^2+3xy+y^2=76\). Consider \(\displaystyle P=\)\(\left( 6, \ 2\right)\). For the short checks \(\displaystyle a=3\).
Find the value of \(\displaystyle x^{2}\)+axy+\(\displaystyle y^{2}\) at the stated point.
Enter one number or fraction. Keep exact values during your working; use at least six decimal places for an approximate final answer. A calculator may be used.