Huaizhong R.

x+x2/2+x3/3+x4/4+...+xn/n and x∈(-1,1)

Let T:R2→R2 be the function defined by T(〈x,y〉) = 〈-y,x〉.Hint: We want to show T(u + v) = T(u) + T(v) and T(λu) = λT(u) For all u,v ∈ R2 and λ ∈ R.

Find a simple function g of the smallest order so that f(x) is big-O of g(x). In your estimation you can use theorems learned in lecture about the big-O estimates of sums/products of functions.f(x)... more

It would seem that one way of proving this would be to show the existence of non-algebraic numbers. Is there a simpler way to show this?

There is a question in my calculus textbook that asks to find a point on the parabola $y^2 = 2x$ that is closest to point $(1,4)$. They want us to first use the distance formula, but then... more

∫∫∫xyz dV where T is is the solid tetrahedron with vertices (0,0,0) (1,0,0) (1,1,0) (1,0,1). How do I figure out what z=f(x,y) is with these points? The equation of a tetrahedron is... more

A function 'f' of two variables is said to be homogeneous of degree 'n' if f(tx,ty) = t^n*f(x,y) whenever t > 0.   How can I show that such a function 'f' satisfies the equation: x*(partial... more

X goes from 0 to 2 Y goes from 0 to sqrt(4-x^2) Z goes from 0 to sqrt(4-x^2-y^2).   The function is zsqrt(4-x^2-y^2)dzdydx.   I know the conversion from rectangular to spherical and the... more

 If A is a square matrix with inverse A-1 and c is a nonzero real number, then  ( cA)-1=1/c A-1    If you think the statement is true, then show that it is true. On the other hand, if you think... more

True or false: If AX = B is a system of n linear equations in n unknowns and A-1 does not exist, then AX = B does not have a unique solution.  Please explain and give example