Derivatives
d/dx (x*2^x)
2^x(1+x ln2)
The speed you should film at to make a 1/z scale model appear realistic when you play back the film at 24 frames per second
24sqrt(z)
Our 3 U of M athletes
Alex, Anthony, and Michael
A function that is continuous but not differentiable
|x|
The limit of Michael Phelps's wetness as the number of pieces of towel goes to infinity
e^(-T)
d/dx (x^2-sinx)/e^x
(e^x(2x-cosx) - e^x(x^2-sinx))/e^(2x)
How we know it's possible to make a fair five-sided die.
A Dorito is a triangular prism which, when tossed, is less likely to land on a rectangular side than a triangular side. A Toblerone bar is the same basic shape, but its rectangular sides are likelier than its triangles. So by the Intermediate Value Theorem, somewhere in between is a fair die.
Has two snails who can paint
Shea
The four ways your textbook would like you to approach every problem
Algebraically, Numerically, Graphically, and with words
d/dt(t^2-t)e^(-t)
(t^2-t)(-e^(-t)) + (2t-1)e^(-t
How and why a slide rule can multiply numbers.
The scales are chosen so that the distance from 1 to x is log(x). So
(dist from 1 to A) + (dist from 1 to B) =
log(A) + log(B) = log(AB) = (dist from 1 to AB)
Almost cut off the tip of her thumb so she could go home from her restaurant job
Hailey
The number of students in Math 115 this semester, to within 100.
1750
d/dx (x^3tanx-e^(5x))/(x+1)
((x+1)(3x^2tanx+x^3sec^2x-5e^(5x))+(1)(x^3tanx-e^(5x)))/(x+1)^2
The amount of water on Michael Phelps if his area is 1, he starts with a liter on him and towels off with a towel of size T split into n parts.
(1/(1+T/n))^n
Two of us who have flown planes
The first and last sections of the book covered by Math 115 Exam 2
The examcovers 2.4 through 4.3. (Note 2.4 is a repeat from Exam 1.)
d/dx(x^x)
d/dx((e^lnx)^x) = d/dx(e^(xlnx))
=(x*1/x + 1*lnx)e^(xlnx)
=(1+lnx)x^x
How to use a record player to convert from Celsius to Fahrenheit.
Suppose the temerature is c degrees Celsius. Set the stopwatch to 32 and the record player to 33 1/3 RPM. Start the stopwatch and stop it after c revolutions.
We have many musicians. Name at least 4, and their instruments.
Allen (8 years of clarinet, also piano & guitar)
Feaven (8 years of violin)
Nick (Cymbals in the MMB)
Noah (8 years of violin)
Olivia (7 years of piano)
Reid (8 years of clarinet)
Zenzi (trombone in the MMB)
How to show that any assignment of the real numbers between 0 and 1 to hotel rooms numbered 1,2,3,... must be incomplete.
Choose digits different from the diagonal entries.