Educator Level
10
Questions Answered
550
Recent Activity

Answered a Question in Math
`dy/dx = (dy/dt)/(dx/dt) = (1/t)/(2t) = 1/(2t^2) `
`(d^2y)/(dx^2) = d/dx(dy/dx) = d/dt(dy/dx) dt/dx `
`=... 
Answered a Question in Math
`n! gt n^2 ` for all n > 3, so except for the first few terms, this series is strictly bounded above by the pseries 1/n^2:

Answered a Question in Math
The Integral test says that this sum will converge if and only if this integral also converges:`int_{1}^{infty} x^k e^{x} dx `

Answered a Question in Math
The Root Test says that this limit will converge if and only if the following limit (actually limit superior) is less than 1:
`C... 
Answered a Question in Math
The Root Test says that this limit will converge if and only if the following limit (actually limit superior) is less than 1:
`C... 
Answered a Question in Math
`sin ((2n1) pi/2)` is a function that alternates from 1 to 1, and is in fact equivalent to `(1)^(n+1)`.
Thus this series... 
Answered a Question in Math
This is just the alternating harmonic series with the first three terms stripped out:
`sum_{n=1}^{infty} (1)^{n+1}/{n+3} =... 
Answered a Question in Math
This is a geometric series, which will converge if and only if `x < k`. It must be strictly less, as the series `(1)^n and...

Answered a Question in Law and Politics
In theory, only Congress has the power to declare war, as written in Article I, section 8 of the Constitution. The President of the...

Answered a Question in Law and Politics
The Electoral College is the actual system by which the President of the United States is elected. The President is not actually...