Rational binomial expansions and validity: check 1
Difficulty: ★★☆Info
Maths4U Original · Short practice
Consider \(\displaystyle \frac{1}{\sqrt{3 x + 1}}\) expanded in ascending powers of x.
Write \(\displaystyle a=3\) and \(\displaystyle r=\)\(\displaystyle - \frac{1}{2}\).
Find the coefficient of x.
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.
Rational binomial expansions and validity: review variant 1
Difficulty: ★★☆Info
Maths4U Original · Short practice
Consider \(\displaystyle \frac{1}{4 x + 1}\) expanded in ascending powers of x.
Write \(\displaystyle a=4\) and \(\displaystyle r=\)\(-1\).
Find the coefficient of x.
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.
Rational binomial expansions and validity: check 2
Difficulty: ★★☆Info
Maths4U Original · Short practice
Consider \(\displaystyle \frac{1}{4 x + 1}\) expanded in ascending powers of x.
Write \(\displaystyle a=4\) and \(\displaystyle r=\)\(-1\).
Find the coefficient of \(\displaystyle x^{2}\).
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.
Rational binomial expansions and validity: review variant 2
Difficulty: ★★☆Info
Maths4U Original · Short practice
Consider \(\displaystyle \frac{1}{\left(5 x + 1\right)^{2}}\) expanded in ascending powers of x.
Write \(\displaystyle a=5\) and \(\displaystyle r=\)\(-2\).
Find the coefficient of \(\displaystyle x^{2}\).
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.
Rational binomial expansions and validity: check 3
Difficulty: ★★☆Info
Maths4U Original · Short practice
Consider \(\displaystyle \frac{1}{\left(5 x + 1\right)^{2}}\) expanded in ascending powers of x.
Write \(\displaystyle a=5\) and \(\displaystyle r=\)\(-2\).
Find the coefficient of \(\displaystyle x^{3}\).
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.
Rational binomial expansions and validity: review variant 3
Difficulty: ★★☆Info
Maths4U Original · Short practice
Consider \(\displaystyle \left(6 x + 1\right)^{\frac{3}{2}}\) expanded in ascending powers of x.
Write \(\displaystyle a=6\) and \(\displaystyle r=\)\(\displaystyle \frac{3}{2}\).
Find the coefficient of \(\displaystyle x^{3}\).
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.
Rational binomial expansions and validity: check 4
Difficulty: ★★☆Info
Maths4U Original · Short practice
Consider \(\displaystyle \left(6 x + 1\right)^{\frac{3}{2}}\) expanded in ascending powers of x.
Write \(\displaystyle a=6\) and \(\displaystyle r=\)\(\displaystyle \frac{3}{2}\).
Find the positive radius of the validity interval.
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.
Rational binomial expansions and validity: review variant 4
Difficulty: ★★☆Info
Maths4U Original · Short practice
Consider \(\sqrt{2 x + 1}\) expanded in ascending powers of x.
Write \(\displaystyle a=2\) and \(\displaystyle r=\)\(\displaystyle \frac{1}{2}\).
Find the positive radius of the validity interval.
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.