I am trying to find an expression for $\sin(40)$ in the following way: Let $\theta$ = 40 3$\theta$=120 $\sin(3\theta)$=sin(120) $-4\sin^3(\theta)+3\sin(\t...

Here is Prob. 45, Sec. 2.3, in the book Calculus With Analytic Geometry by George F. Simmons, 2nd edition: Find the point on the graph of $y = x^2$ that i...

suppose we have the following: $y=(2x+1)^7$ and we want to integrate it, then we set $u = 2x+1$ but then.....$du = 2dx$..... logically speaking now, du an...

Right, so I'm to find the definite integral (interpreting it as an area)... $\int^0_{-3}(1+\sqrt{9-x^2})dx$ How do I go about doing this? I am to spe...

How do you determine whether the quadratic form $Q(x,y) = 2x^2 - 4xy + 5y^2$ is positive definite, negative definite, or indefinite? Could someone show st...

If we multiply or divide an inequality by a negative number, the inequality symbol is reversed. Why is this true? Example: Given $1<2,$ multiplying bot...

I need to find the inverse Laplace transform of the following function: $$ F(s) = \frac{(s-2)e^{-s}}{s^2-4s+3} $$ I completed the square on the bottom and...

We can cut up circles in whatever size chunks we choose -- we normally choose to cut them up so that the size of the angle of an entire circle is $2\pi$ o...

I am reading Hoffman and Kunze linear algebra book. In chapter $8$ there is a theorem that states as " Let $V$ be a finite-dimensional complex inner produ...

So I'm sure you have all heard of the number $e$ which is approximately $2.71828...$ . But why is it called $e$? It isn't due to Leonhard Euler,...