Is the following true? Let $x_n$ be a sequence with the following property: Every subsequence of $x_n$ has a further subsequence which converges to $x$. T...

find polar area (inner loop): $r=1+2sin(\theta)$ I get that the zeros occur at $\frac {7\pi}{6} and \frac {11\pi}{6}$ and in turn this should be where the...

I have the following question about matrices, Let $S$ and $A$ be two $n \times n$ matrices which are respectively symmetric and anti-symmetric. Can I conc...

The horizontal line test seems to show that no horizontal line intersects the graph of $f$ at more than one point. However, the textbook tells me it'...

I've only seen the bump function $e^\frac1{x^2-1}$ so far. Where could I find examples of functions $C^∞$ on $\mathbb{R}$ that are zero everywhere ex...

Use de-Moivre's theorem to find the reciprocal of each number below. $$\sqrt 3 - i$$ Given $\sqrt{3}-i$ , we need to find the reciprocal of it using ...

I'm tasked with computing the circulation of the vector field $\vec F = <y^2, z, xy>$ along the triangle with vertices $(1,0,0), (0,1,0), (0,0,...

How do we denote the direct sum of non-orthogonal vector spaces? Is there a symbol for that?

The commutative law of multiplication states that: If '$a$' and '$b$' are any whole numbers, then '$a · b = b · a$'. I'...

I am using an FFT to multiply polynomials. Because I want the program to be as fast as possible I am leaving away the zero padding. For example, if we wan...