Let n be a positive integer and suppose f is continuous on [0,1] and f(0) = f(1). Prove that the graph of f has a horizontal chord of length 1/n. In other words, prove there exists x \in [0,(n - 1)/n] such that f(x+1/n) = f(x)
8. Let f : R^3 → R a function all whose first order partial derivatives are continuous and such that f(0, 1, 1) = 0,
f_x(0, 1, 1) = 1, f_y(0, 1, 1) = 2, f_z(0, 1, 1) = 3. Find lim
t-->0
f(t2, cosh t, et)
f(t, cos t, cosh t)
9. Let f : R2 → R such that f(x, y) = f(y,−x) for all (x, y) ∈ R2, and...
So I'm taking a freshan analysis class. I've never covered converting things to binary and other number systems before, and in a chapter about sequences the book mentions binary and has an exercise to convert the square root of two to six decimal places. Can someone tell me what binary is and to...
Sligtly more complex than the average one, I'd assume. How would I go about proving that the limit of of a rational expression consisting of two polynomials of the same degree goes to one and the limit of one where the degree of the bottom is greater than the degree of the top goes to zero. I'd...
yes? no? just let me preemptively thank you all for all the help you've given me thusfar and for all the help you might choose to give me in the future. you guys rock!
how does i<0 relate to a_i. like a_i seems to me to be just a constant, with the _i part just differenting it from other as. when they say that i<0 do they mean that a_i <0?
and am i correct in saying that all of the elements of F are (a_-nx^-n,...,a_0x^0,a_1x,a_2x^2,...,a_nx^n)? and the as...
to reiterate: i honestly have no clue where to start and I'm not even sure i understand the problem correctly.
to give you a clue as to where the class is mathematically: it's a class for people who might want to be math majors (or minors), so pretty much everyone in it is a freshman in one...
I have absolutely no clue how to start here.
Let F be the set of expressions of the form a = sum from i in Z of a-sub-i*x*i, where each a-sub-i is an element of R and {i < 0 : a-sub-i does not equal 0) is finite. (X is a formal symbol, not a number). An element a belonging to F is positive if...