Taylor Problems
Maclaurin Problems
Maclaurin Extra
Concepts
Fun
100
The formula for the Taylor Series.
f(x) = f(a) + f'(a)(x-a) + f''(a)(x-a)2/2! + f'''(a)(x-a)3/3! + ...
100
The formula for the Maclaurin Series.
f(x) = f(0) + f'(0)x + f''(0)x2/2! + f'''(0)x3/3! + ...
100
The Maclaurin Series of cos(x), given sin(x) = x - x3/3! + x5/5! - x7/7! + ...
cos(x) = 1 - x2/2! + x4/4! - x6/6! + ...
100
A special case of a Taylor series that is centered around the value a=0.
What is a Maclaurin Series?
100
What is the name of this celebrity
Taylor Swift
200
The Taylor Series for cos(x) centered around a = π/2
cos(x) = -(x-π/2) + (x-π/2)3/3! - (x-π/2)5/5! + ...
200
The Maclaurin Series of ex.
What is 1+ x + x2/2! + x3/3! + x4/4! ...
200
The Maclaurin Series of cos(x2), given cos(x) = 1 - x2/2! + x4/4! - x6/6! + ...
cos(x2) = 1 - x4/2! + x8/4! - x12/6! + ...
200
The most commonly used functions for Taylor Series.
What are ex, sin(x), cos(x), ln(x)?
200
What is the name for the profession where a person makes fitted clothes to fit individual customers.
"Tailor"
300
The Taylor Series for x3 + 2x2 - 5x centered around a=2
6 + 15(x-2) + 8 (x-2)2 + (x-2)3
300
The Maclaurin Series for 1/(1-x)
1 + x + x2 + x3 + x4 + ...
300
The Maclaurin Series for xcos(x), given cos(x) = 1 - x2/2! + x4/4! - x6/6! + ...
xcos(x) = x[1 - x2/2! + x4/4! - x6/6! + ...] = x - x3/2! + x5/4! - x7/6! + ...
300
The definition of a Taylor Series.
A series made up of an infinite sum of derivatives of a function and can represent that function around a point "a".
300
Taylor Heinicke
400
The Taylor Series of ln(x) centered around a=1
ln(x) = (x-1) - (x-1)2/2 + (x-1)3/3 - (x-1)4/4 + ...
400
The Maclaurin Series for 1/(1+x)
1 - x + x2 - x3 + x4 - ...
400
The Maclaurin Series of f(x), f(x) = x2e-x, given ex = 1 + x + x2/2! + x3/3! + ...
f(x) = x2e-x = x2[1 - x + x2/2! - x3/3! + ...] = x2 - x3 + x4/2! - x5/3! + ...
400
The step to simply coefficients on the numerator and factorials in the denominator. Example: 4(x-c)3/3!
Split the factorials. 3! = 3x2x1. Then simplify 4(x-c)3/3x2x1 by simplifying 4/2 into 2 to equal 2(x-c)3/3
400
What is the price of this Mclaren Senna
1 - 1.2 million dollars
500
The Taylor Series for sin(x) centered around a=π
sin(x) = -(x-π) + (x-π)3/3! - (x-π)5/5! + ...
500
The Maclaurin Series for ln(1+x)
x - x2/2 + x3/3 - ...
500
The Maclaurin Series for cos2(x), given cos(x) = 1 - x2/2! + x4/4! - x6/6! + ..., and the power reducing formula for cos2(x) = [1+cos(2x)]/2
cos(2x) = 1 - 4x2/2! + 16x4/4! - 64x6/6! + ...,
cos2(x) = [1 + (1 - 4x2/2! + 16x4/4! - 64x6/6! + ...)]/2
= [2 - 4x2/2! + 16x4/4! - 64x6/6! + ...)]/2
= 1 - 2x2/2! + 8x4/4! - 32x6/6! + ...
500
Shortcut used to find the Maclaurin series of cos(x) using Maclaurin series of sin(x).
Take the derivative of both sides.
500
What is the first name of the Mathematician who invented "Taylor Series"
James Gregory or Brook Taylor