Small increments and approximations: check 1
Difficulty: ★★☆Maths4U Original · Short practice
Let \(y=3 x^{3}\). The value of x increases from \(2\) by \(\frac{1}{21}\).
Estimate the increase in y using differentials.
Enter one exact number or fraction. These checks support non-calculator practice. Give full reasoning separately for written problems.
Small increments and approximations: review variant 1
Difficulty: ★★☆Maths4U Original · Short practice
Let \(y=4 x^{4}\). The value of x increases from \(3\) by \(\frac{1}{22}\).
Estimate the increase in y using differentials.
Enter one exact number or fraction. These checks support non-calculator practice. Give full reasoning separately for written problems.
Small increments and approximations: check 2
Difficulty: ★★☆Maths4U Original · Short practice
Let \(y=4 x^{4}\). The value of x increases from \(3\) by \(\frac{1}{22}\).
Find the exact increase in y.
Enter one exact number or fraction. These checks support non-calculator practice. Give full reasoning separately for written problems.
Small increments and approximations: review variant 2
Difficulty: ★★☆Maths4U Original · Short practice
Let \(y=2 x^{2}\). The value of x increases from \(4\) by \(\frac{1}{23}\).
Find the exact increase in y.
Enter one exact number or fraction. These checks support non-calculator practice. Give full reasoning separately for written problems.
Small increments and approximations: check 3
Difficulty: ★★☆Maths4U Original · Short practice
Let \(y=2 x^{2}\). The value of x increases from \(4\) by \(\frac{1}{23}\).
Estimate the new value of y.
Enter one exact number or fraction. These checks support non-calculator practice. Give full reasoning separately for written problems.
Small increments and approximations: review variant 3
Difficulty: ★★☆Maths4U Original · Short practice
Let \(y=3 x^{3}\). The value of x increases from \(5\) by \(\frac{1}{24}\).
Estimate the new value of y.
Enter one exact number or fraction. These checks support non-calculator practice. Give full reasoning separately for written problems.
Small increments and approximations: check 4
Difficulty: ★★☆Maths4U Original · Short practice
Let \(y=3 x^{3}\). The value of x increases from \(5\) by \(\frac{1}{24}\).
Estimate the percentage increase in y.
Enter one exact number or fraction. These checks support non-calculator practice. Give full reasoning separately for written problems.
Small increments and approximations: review variant 4
Difficulty: ★★☆Maths4U Original · Short practice
Let \(y=4 x^{4}\). The value of x increases from \(2\) by \(\frac{1}{20}\).
Estimate the percentage increase in y.
Enter one exact number or fraction. These checks support non-calculator practice. Give full reasoning separately for written problems.