ws07 - WORKSHEET 7 - Fall 1995 1. Let f (x) = x3 + 3x2 3x....

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WORKSHEET 7 - Fall 1995 1. Let f ( x )= x 3 +3 x 2 - 3 x . a) At any point ( x 0 ,y 0 ) on the graph, what is the slope of the tangent line to the graph? b) The graph of f ( x ) has two tangent lines parallel to the line y =6 x + 100. Find the equations of these two lines. 2. a) Find all points on the graph of y = x 2 whose tangent lines pass through the point (5 , 0). b) Show that no line tangent to the graph of f ( x )= x + 1 x passes through the origin. 3. In worksheet 5, you used the Squeeze Theorem to show that lim θ 0 sin θ θ =1 . (1) Recall that in the process of proving that (sin θ ) 0 =cos θ we used limit (1) and lim θ 0 1 - cos θ θ =0 . (2) The goal of this problem is to prove limit (2). The diagram below will be helpful. 1 OA Θ B P a) We will only consider approaching 0 through positive angles, that is we are computing a right-hand limit. Prove that this is sufficient by showing that the left-hand limit must be the same. (Hint: is cosine an even or odd function?) b) Triangle
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ws07 - WORKSHEET 7 - Fall 1995 1. Let f (x) = x3 + 3x2 3x....

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