151_review2-1

# 151_review2-1 - Review Problems for exam 2 Note these are...

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Review Problems for exam 2 Note: these are additional problems. The problems on your exam may be very diﬀerent from these ones. You can watch the solutions for the problems with (*) on the posted streaming power points. 1. Use implicit diﬀerentiation to ﬁnd the equation of the tangent line to the curve at the given point. (a*) x 3 - y 3 = cos xy + 7 , (0 , - 2) (b) x 3 + y 3 - 9 2 xy = 0 , (2 , 1) 2*. if y = x x 2 ﬁnd dy dx 3. Find the absolute maximum and absolute minimum values of the function on the given interval. (a) f ( x ) = 2 x 3 - 3 x 2 - 12 x + 1 , [ - 2 , 3] (b*) f ( x ) = xe - x , [0 , 2] 4. For a given function: ﬁnd its domain, its vertical and horizontal asymptotes (if any), where it is increasing and decreasing and where it is concave up and down. Find all local maximum and minimum and all inﬂection points. Use this information to sketch the graph of the function. (a*) f ( x ) = 2 x - 6 x - 1 (b*) f ( x ) = x ln x (c) f ( x ) = xe x 5. Evaluate each of the following limits.

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151_review2-1 - Review Problems for exam 2 Note these are...

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