I find that the quotient rule is easier to work with algebraically, since you already have the lcd(which is the first step of simplifying a derivative found by the using the product on quotient.) Also, if you are interested in zeros/critical points, the quotient rule saves you steps on your...
I assumed that the belt goes from north pole to north pole (south pole to south pole) and thus the length of belt that gets accounted for being in contact with the pulleys would be half of the sum of the circumferences of the pulleys. I do not know enough about pulleys to know if and how to...
Well, I do not know specifics about pulleys so some of my math or assumptions might be wrong, but here goes nothing.
Assume we have pulleys with radii R,r respectively such that R>r.
Assume we have a belt with radius p, thus length P= 2p\pi.
Let c be the distance from the tops(bottoms) of...
Careful, you are mixing apples and oranges. The max(min) will be the value of Y which is bigger(smaller) than every other value of Y for some region around your max(min) value.
Not X like you said, X is the input variable that determines your Y.
You should try graphing ax^2 + bx + c for...
the way i translated it was "if the area of the smallest big rectangle is not equal to the area of the biggest small rectangle, then the function is not Riemann integrable"
Maybe I am missing something, but if we have shown that 1 is a power of 2, and for some natural number k=>1, we are assuming k is a sum of powers of 2, wouldn't k+1 necessarily be of the correct form since we are adding a power of two to a finite sum of powers of two we are left with a finite...
Why not try looking at a circle of radius one centered at the origin, counting the points of interest there? Then look at a circle of radius 2 centered the origin, and count those points. Then a circle with radius 3, a circle with radius 4, radius 5, ..., radius n, and maybe you will be able to...
because the solutions form a 2-dim vector space over the field of complex numbers, so by properties of vector spaces all scalar multiples are elements of said solution space, which in this case would include linear combinations of complex conjugates
It is stated in almost every linear algebra text i could find that the inverse of a triangular matrix is also triangular, but no proofs accompanied such statements.
I am convinced that it is the truth, but I have not been able to write anything down that I am satisfied with that doesn't rely...
you could draw a quadrant of a circle of radius 6 and check the number of points there and multiply that number by four, being careful not to double count points that lie on the axis,
as for a closed form, i would be surprised if one did not exist...
Side note
Wolfram indeed does have a...
I have to agree with tyroman, something that I have picked up from my teachers and has helped my white/chalk board writing, its give yourself points of reference.
For example, one teacher I have teaches in a classroom with two chalkboards laid side by side along the same wall.
Every time...
My favorite teachers have been the ones i consider consistent. You know that what you get from them monday is what you are going to get every monday, and everyday for that.
Classroom management is one of the hardest things for any teacher to master. I feel that if a teacher's personality can...
Maybe our definitions of convolutions are different, but the definition I have learned for the convolution of two functions is defined by an integral, i.e. $ f*g(t)=\int_{0}^{t}f(u)g(t-u)du.$ Letting $v=t-u,$ then $dv=-du$($t$ is constant with respect to $u$). We also need to change our limits...