Flashcards
Maclaurin Series
Cards in this deck (11)
- 1The Maclaurin Series is a way to......Calculate some general functions using a series of polynomial functions
- 2sin x = ......x - (x^3 /3!) + (x^5 /5!) - (x^7 /7!) + ....
- 3cos x = .....1 - (x^2 /2!) + (x^4 /4!) - (x^6 /6!) + ....
- 4e^x = ....1 + x + (x^2 /2) + (x^3 /3) + .....
- 5sin x , cos x and e^x work for which values of x?All of them
- 6ln(1+x) = ....x - (x^2 /2) + (x^3 /3) - (x^4 /4) + ....
- 7(1+x)^n = ....1 + nx + (n(n-1)x^2)/2! + (n(n-1)(n-2)x^3)/3! + ....
- 8ln(1+x) and (1+x)^n only work for what values of x?-1 < x ≤ 1
- 9If for our values of x we have something like -1<4x≤1 , what must we do?Divide through by 4
(-1/4 - 10Find the first 4 terms for ln(1+3x) and write down the values of x it's valid for.ln(1+x) = x - (x^2 /2) + (x^3 /3) - (x^4 /4) + ....
ln(1+3x) = (3x) - ((3x)^2 /2) + ((3x)^3 /3) - ((3x)^4 /4) + ....
Simplifies to: 3x - (9x^2)/2 + (27x^3)/3 - (81x^4)/4 + .....
-1<3x≤1 , so -1/3 - 11Be sure to check questions on Maclaurins series to find a important exam questions on......Multiplying together 2 series