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Math · Calculus
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2, Evaluate the limit r lim, o ex lny. Evaluate the limit mu (Hint: Factor the numerator, then use direct substitution). a. Prove that the limit does not exist by considering the two paths given below approaching the point (0, 0) for (xy) (0,0 x +y Use the path wherex Use the path where x y Find for (xy) for foxy) y 2x (I. Find the total differential of 2x y. 12 Given z ln(x +y y?)... (a) opproxi the change in: asa, nmoves from Co. )to the point (0.01, 0.98). a) Find the actual change in as moves from (0,1) to the point o.01.098. The height and radius of a right circular cylinder are approximately 15 centimeters and 8 centimeters, respectively. The maximum error in each measurement is t0.02 centimeters. (a) Find the approximate volume of the cylinder hint: V Cr, h) z Trnh, tind VCBIS) (b) Use the total differential to estimate the propagated error in the calculated volume of the cylinder dy (e) Use the total differential to estimate the relative error in the calculated volume of the cylinder and express this relative error in percent dV

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