16A-HW2 - Math 16A, Spring 2010 HW2, Apr-30-10 Due by...

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Math 16A, Spring 2010 HW2, Apr-30-10 Due by May-7-10. I will collect HW2 in class We will grade randomly one of the following exercises: 1. Analyze the domain, continuity (and say if a discontinuity point is removable or not), V.A. and H.A. of the following function f ( x ) = x x + 2 x 3 - x 2 - 2 x 2. Analyze the domain, continuity (and say if a discontinuity point is removable or not), V.A. and H.A. of the following function f ( x ) = | x - 2 | 2 x - 4 when x < 4 1 4 when x = 4 - x 2 4 x 2 - 24 x when x > 4 3. Find the slope of the tangent line to the following functions at the point P = ( x 0 ,f ( x 0 )): -Using the definition m 0 = f 0 ( x 0 ) = lim Δ x 0 f ( x 0 + Δ x ) - f ( x 0 ) Δ x - and then using the power rule ( d dx x n = nx n - 1 ), and the linearity of the derivative ( d dx [ af ( x ) + bg ( x )] = af 0 + bg 0 with a,b = number ) example f ( x ) = 2 x 2 , x 0 = 3 . Using the definition we get f 0 ( x ) = lim Δ x 0 2( x + Δ x ) 2 - 2 x 2 Δ x = 4 x f 0 (3) = 12 1
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16A-HW2 - Math 16A, Spring 2010 HW2, Apr-30-10 Due by...

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