Mathematica cannot seem to do it,
It can solve y'' = 1/y
The solution is
e to the power of a complicated function of the Inverse of the intergral of e^-(x^2)
I cannot see how multiplying by x^3 would make it easier.
I would bet a reasonable sum of money on it being a misprint.
you can use a t test just like you do in simple linear regression,
except the degrees of freedom is n-3 not n-2,
You can test each variable separately.
you have to be careful about any conlcusions you make for example if x1 and x2 are highly correlated.
I saw a first year question solve y''=x^3/y
I am assuming that this is a misprint because
solving y'= x^3/y is easy because it is separable
but I have no idea how to solve
y'' = x^3/y
a car of mass m is traveling around a banked track.
if F is the friction force up the track and x is the angle of the track
I say
F= mg sin(x)- mv^2/r cos(x)
N = mg cos(x) + mv^2/r sin(x)
but both my books say
F= mg sin(x)- mv^2/r cos(x)
N = mg cos(x) - mv^2/r sin(x)
I am teaching a student in a course without partial differentiation so
I can only think of the following method
let b be a constant and set y=b so
xb= exp(x-1) +blnb
means b= exp(x-1) which means x = lnb+1
now d(xb)/dx= b
and d(exp(x-1)+blnb)/dx = exp(x-1)
so if x > lnb+1
xb>...
Gokul I am embarassed at my typos, I will fix them
As for the dilema of students being used to only have one answer, If you
if you are in R3 and say x=0 you can ask the students what values y and z can take and they don't know, when you say y and z can take any value they don't believe you...
Does anyone have sample wrong answers for the multiple choice test I was writing in the first post?
I offer a warning to people that will teach that subject. The that bottom half of the class does not believe you initially when you say x=0 is a plane in R3. The idea that y and z can take any...
OK I will explain the questions to prove I am not a liar
x+y=5
can be represented in RREF as (1 1 |5)
y is a non leading varible ( a free variable)
let y =t
so x+ t = 5
x=5-t
to summarize)
(x,y) = (5-t , t)
this is the same as
(x,y) = (5,0) + (-1,1)t
This a line in R2
Moving on to...
I teach first year uni students and they don't seem to know what is a plane
and what is a line in 3d. I have been paid to make an online multiple choice
a prototype is given below. Any help would be appreciated
1)x+y=5
(a) has infinite solutions
examples of solutions are (-1,6), (0,5)...
You only need to prove that appling simpsons rule to x^3 gives the same answer as integration.
Thi
It should be clear that if simpsons works for both polynomials p(x) and q(x) then it works for p(x)+ q(x). Because int (p(x)+q(x)) = int(p(x)) + int(q(x))
and the same rule applies to...
sin(x)/cos(x) = tan(x)
to see why this is true Draw a right triangle with hypotenuse 1 and an acute angle x, you can work the sides of the right triangle have lengths sin(x) and cos(x).