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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 (...

Step 1: find the asymptotesThere are two kinds of asymptotes we look for: vertical and horizontal.The vertical ones happen when y goes to negative...

Letting z be the complex number cos x + i sin x, we will use the identities (zⁿ + 1/zⁿ) = 2 cos nx and (zⁿ - 1/zⁿ) = 2i sin nx. Both of these follow from De Moi...

Set up the auxiliary equation by letting (dy/dx) = m
So we have: m² + 3m + 2 = 0
Solve for m and we get: (m+1)(m+2) = 0Therefore, m₁=-1 and m₂=-2
Now we s...

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=...