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a) x^(2) + 6x + 1 = 0 (x + 3)^(2) - 8 = 0 x = - 3 + sqrt(8) or x = - 3 - sqrt(8)

b) (x-5)(x+1) = 0 x = -1 or 5

c) using answer to part b: (x-5)(x+1) < 0 draw its graph then: -1<x<5<...

integrating a product of functions of x - integration by parts. integral of uv' = uv - integral of u'v. choice of u from LIATE - logs, inverse trig, algebra, trig, exponentials - choose u=x. u=x, v'=e^(-x...

If the lines intersect the position vectors r_1 and r_2 must be equal at the point of intersection, so: (1,-1,2)+a(-1,3,4)=(c,-4,0)+b(0,3,2) which gives three equations for the three components: 1-a=c, -1...

2x + 3

This question is to be done by integration by parts because it has "two types" of integrals. To perform integration by parts, we need to first split the function into its two parts, producing x ...