PracticeMidterm2 - one solution in the interval [-1 , 1]....

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Practice Midterm 2 1. Find dy dx . a) y = e x 3 +1 b) y = log x (cos x ) c) y 2 + 6 xy + x 2 = 7 2. A point q is moving along the parabola y = x 2 . Find the rate of change of the distance of the point from the origin in terms of x and dx dt . 3. Find an approximate value for sin 1 4. Evaluate the following limits. a) lim b 2 b 2010 - 2 2010 b - 2 b) lim n →∞ ± 1 + 5 n ² n c) lim x 2 - x 2 - 4 x - 4 - x 5. Let c be a real number. Show the equation x 5 - 6 x + c = 0 has at most
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Unformatted text preview: one solution in the interval [-1 , 1]. 6. Sketch the graph of y = x 1+ x 2 , labeling asymptotes, local extrema, points of inection, and regions where the function is increasing, decreasing, concave up, and/or concave down. 7. Find the maximum value of f ( x ) = 1 ( x 4-8 x 2 + 17) 2...
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