# 2nd - Calculus With Analytic Geometry Hakan TOR March...

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Calculus With Analytic Geometry Hakan TOR March 4,2010 1. The graph of g is given. (a) At what numbers is g discontinuous? Why? (b) At what numbers is g not diﬀerentiable? Why? Solution: (a) Although lim x →- 2 - g ( x ) = lim x →- 2 + g ( x ), the function g ( x ) is discontinuous at the point - 2 because lim x →- 2 g ( x ) 6 = g ( - 2). Since g (5) = lim x 5 - g ( x ) 6 = lim x 5 + g ( x ), g ( x ) is discontinuous at the point 5. Remark Although -∞ = lim x 2 - g ( x ) 6 = lim x 2 + g ( x ) = , we can not say any thing about continuity of g , because the point 0 is not in the domain of g . (b) Since g is discontinuous at the points -2 and 5, g is not diﬀerentiable at that points. The function g is also not diﬀerentiable at the point 2. 2. The normal line to a curve C at a point P is, by deﬁnition, the line that passes through P and is perpendicular to the tangent line to C at P. Find an equation of the normal line to the parabola y = 1 - x 2 at the point (2 , -

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2nd - Calculus With Analytic Geometry Hakan TOR March...

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