pnrjulius
eNotes EducatorAchievements
10
Educator Level
563
Answers Posted
196
Answers Bonused
About
With a bachelor's degree in cognitive science and a master's in economics, I think of myself as a cognitive economist. I write a blog called Human Economics which updates twice a week. I have several years of experience tutoring in a variety of subjects, particularly math, science, economics, and Latin, to students ranging from middleschoolers to college students to adults going back for their GED.
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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 ` `= 1/2 t^{3} (1/(2t)) = 1/(4t^4)` This is always positive, so the function is concave... 
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:`sum_{4}^{infty} 1/{n!} lt sum_{4}^{infty} 1/n^2` Finitely many terms... 
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 ` When integrating this, we would use integration by parts, and we... 
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 = lim_{n rightarrow infty} {n!}/{n^n}^(1/n)` `C = lim_(n>oo)... 
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 = lim_{n rightarrow infty} (n!)^n/(n^n)^2^(1/n)` This is actually a...
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