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It can be shown that the equation of any plane can be given by r.n=a.n, where r = xi + yj + zk, n is a direction vector normal to the plane, and a is any point vector on the plane. a can be found easily (thr...

Step 1: find the asymptotes There are two kinds of asymptotes we look for: vertical and horizontal .The vertical ones happen when y goes to negative or positive infinity, which is when the denominator of the...

Letting z be the complex number cos x + i sin x, we will use the identities (z n + 1/z n ) = 2 cos nx and (z n - 1/z n ) = 2i sin nx. Both of these follow from De Moivre’s theorem and the odd and even proper...

Set up the auxiliary equation by letting (dy/dx) = m So we have: m 2 + 3m + 2 = 0 Solve for m and we get: (m+1)(m+2) = 0Therefore, m 1 =-1 and m 2 =-2 Now we see we have 2 different real numbers as the solut...

First we check the formula for our first case, n=1 where (cosx + isinx) n =cosnx + isinnx (cosx + isinx) 1 = cos(1x) + isin(1x) - holds true for n=1 next we assume true for our case n=k(cosx + isinx) k = cos...