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Consider the function f(x) = sinx near X = I. Find the linear approximation error when using the linear approximation to estimate sin3. O a.) 0.1416 O b.) -0.1416 ( c.) 0.0005 O d.) -0.0005\fA box in the shape of a cube is to be manufactured with side lengths of 54 cm. Use differentials to estimate the maximum error in the calculated volume of the box if the possible error in measuring the side is 0.5 cm. Given xcosy -x~ + 2y~ =25, compute dy dx a.) dy 2x - cosy = O dx xsiny + 4y b.) dy_ 2x - cosy + 25 O dx - xsiny + 4y c.) dy = 2x - cosy O dx - xsiny + 4y d.) dy = 2x O dx - siny + 4yUsing logarithmic differentiation, find the derivative of Vx5 -3 y = x2 -25 a.) dy A 5x4 2x = + O dx X 3(x5 -3) x2-25 b.) dy A 5x4 2x + O dx X 3(x5 - 3) x- -25 C.) dy x4 V x- 3 5x4 2x = O dx X 2 25 X 3(x5 - 3) x2 -25 d.) dy x4 8 x5 - 3 5x4 2x O dx x- - 25 X 3(x5 -3) x2 -25All sides of a square are increasing at a rate of 4 centimeters per second. How fast is the area changing when each side is 10 centimeters? 3 Sand is falling on a conical pile at the rate of 8 mm' If the height of the pile is always 3 times the radius, find the rate at which the radius is changing when the radius is 5.5 feet. a.) drz 32 ft dt 363W mm _ 32 ft 363 mm = 321T ft 363 mm