Power Series
The number of terms in a Maclaurin/Taylor expansion to exactly equal the original function.
What is oo ?
abs(4+3i) is equivalent to this value.
What is 5?
Re[3e^(i(npi)/2)] is equivalent to __, where n is an odd integer.
What is 0?
[[1,2],[2,3]][[2,0],[0,1]]
is equal to this matrix.
What is [[2,2],[4,3]] ?
The eigenvalues of [[2,0],[0,3]]
What are 2 and 3 ?
The first 3 terms of the Maclaurin expansion of f(x) = e^(2x)
What is 1+2x+2x^2 ?
True or False: x+yi can only be represented by one unique pair of r and theta.
False
1/(i+1)^2 is equal to this cartesian value.
What is -i/2 ?
Det([[0,1,3],[2,3,0],[4,3,2]]) is a dumb way to write this real number.
What is -22 ?
The eigenvectors of [[2,0],[0,3]]
What is c_1[[1],[0]],c_2[[0],[1]] ?
The first 3 terms of the Taylor expansion of 1/(1-x) at a=-1.
What is 7/8+1/2x+1/8x^2 ?
re^(itheta) is the polar form of these cartesian coordinates (A certain mathematician's formula might help).
What is cos(theta)+isin(theta) ?
e^(pisqrt2e^(ipi/4)) is equivalent to this real number.
What is -e^pi ?
[[pi,chi,1],[tau,t,e],[3,sqrt2,9]][[1],[0],[0]] is equivalent to this vector.
What is [[pi],[tau],[3]] ?
The lim_(n->oo)S_n, where the second and third terms of the geometric series are 6 , then 3 .
What is 24 ?
sqrt2e^(-i(3pi)/4) is the polar form of the cartesian coordinate _____.
What is -1-i ?
True or False: -re^(itheta)=re^(i(theta+pi))
True
[[1,3],[-2,4]][[x_1],[x_2]]=[[5],[10]]
"Find" [[x_1],[x_2]].
What is [[-1],[2]]
a_1x+b_1y=c_1
a_2x+b_2y=c_2
x is this solution, given by Cramer's rule.
What is x=Abs([[c_1,b_1],[c_2,b_2]])/Abs([[a_1,c_1],[a_2,c_2]]) ?
The first 2 terms of the approximation for ln((x+1)^(1/x)) (assuming x is small).
What is 1-x/2 ?
The first two non-zero terms in the Maclaurin expansion of cosh(x) .
What is 1+x^2/2 ?
(x+yi)^2=2i is a suitable equation for this relation of x and y.
What is x=y ?
(2hatx+haty-hatz)xx(-4hatx+3haty+hatz) is another way of writing this vector.
What is (4hatx+2haty+10hatz) ?
[[cos(theta),-sin(theta)],[sin(theta), cos(theta)]] is a matrix that performs this type of geometric translation.
What is rotation?