MAT137Y1 Midterm: 2005 Test 2 solution

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10 Apr 2012
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MAT137Y1 Full Course Notes
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Mat 137y, 2005 2006 solutions to term test 2. 1. (10%) (a) find a constant k for which sinx x kx3 x5 lim x 0 exists and the limit is also non-zero, and determine the value of the limit. Regardless of the value of k, the limit is of the form ( 0. The resulting limit does not exist unless the numerator goes to zero, which occurs when k = 1. 120 (10%) (b) find the equation of all tangent lines to the curve y = x2 that intersect the point ( 1. Suppose the tangent line intersects the curve at the point (a,a2). Using two different ways to obtain the slope of the tangent line, we have: is not on the curve. 4 , 3 m = a2 + 3. The corresponding slopes are m = 2a = 3, 2. Therefore the equations of the tangent lines are (cid:18) (cid:19) y + y +

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