Finite expansions as approximations: keep the remainder: check 1
Difficulty: ★★☆Maths4U Original · Short practice
Use terms through \(x^2\) in \((1+x)^5\) to approximate \((1.02)^5\). Enter the approximation.Enter one number or fraction. Round decimals to at least six decimal places when needed.
Finite expansions as approximations: keep the remainder: check 2
Difficulty: ★★☆Maths4U Original · Short practice
Use \(1-4x+6x^2\) to approximate \((0.97)^4\).Enter one number or fraction. Round decimals to at least six decimal places when needed.
Finite expansions as approximations: keep the remainder: check 3
Difficulty: ★★☆Maths4U Original · Short practice
For small positive \(x\), does \(1+4x+6x^2\) overestimate or underestimate \((1+x)^4\)?Choose one answer.
Finite expansions as approximations: keep the remainder: check 4
Difficulty: ★★☆Maths4U Original · Short practice
Why is the expansion of \((1+x)^5\) a finite polynomial?Choose one answer.
Finite expansions as approximations: keep the remainder: review variant 1
Difficulty: ★★☆Maths4U Original · Short practice
Use terms through \(x^2\) in \((1+x)^3\) to approximate \((1.02)^3\).Enter one number or fraction. Round decimals to at least six decimal places when needed.
Finite expansions as approximations: keep the remainder: review variant 2
Difficulty: ★★☆Maths4U Original · Short practice
Use \(1-4x+6x^2\) to approximate \((0.98)^4\).Enter one number or fraction. Round decimals to at least six decimal places when needed.
Finite expansions as approximations: keep the remainder: review variant 3
Difficulty: ★★☆Maths4U Original · Short practice
At x=0.1, find the omitted part when \((1+x)^4\) is approximated by \(1+4x+6x^2\).Enter one number or fraction. Round decimals to at least six decimal places when needed.
Finite expansions as approximations: keep the remainder: review variant 4
Difficulty: ★★☆Maths4U Original · Short practice
What is the greatest exponent of x in the finite expansion of \((2+x)^7\)?Enter one number or fraction. Round decimals to at least six decimal places when needed.