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13 Nov 2019
Q.6 Show that x2 sin () , if x 0 If x = 0. is differentiable at r 0 and find f'(0). Q.7 Find dy/dt when r = 1 if y = x2 + 7-5 and dr/dt 1/3. Q.8 Verify that the curves a4 and23 meet orthogonally. Hint: Curves are orthogonal if the slopes of tangents to the given curves at the point of intersection are perpendicular to each other.) Q.9 Suppose that the differentiable function y = g(x) has an inverse and that the graph of g passes through the origin with slope 2. Find slope of the graph of g1 at the origin. Q.10 Sand falls from a conveyor belt at the rate of 10m2 /min onto the top of a conical pile. The height of the pile is always three-eighths of the base diameter. How fast are the (a) height and (b) radius changing when the pile is 4m high? Answer in centimeters per minute. Q.11 The diameter of a tree was 10 in. During the following year, the circum- ference increased 2 in. About how much did the trees diameter increase? The trees cross-section area? Q.12 Determine the values of constants a, b, c, and d so that f(x) = ar't ba2+cz+d has a local maximum at the point (0,0) and a local minimum at the point (1,-1). ===All the Best!--
Q.6 Show that x2 sin () , if x 0 If x = 0. is differentiable at r 0 and find f'(0). Q.7 Find dy/dt when r = 1 if y = x2 + 7-5 and dr/dt 1/3. Q.8 Verify that the curves a4 and23 meet orthogonally. Hint: Curves are orthogonal if the slopes of tangents to the given curves at the point of intersection are perpendicular to each other.) Q.9 Suppose that the differentiable function y = g(x) has an inverse and that the graph of g passes through the origin with slope 2. Find slope of the graph of g1 at the origin. Q.10 Sand falls from a conveyor belt at the rate of 10m2 /min onto the top of a conical pile. The height of the pile is always three-eighths of the base diameter. How fast are the (a) height and (b) radius changing when the pile is 4m high? Answer in centimeters per minute. Q.11 The diameter of a tree was 10 in. During the following year, the circum- ference increased 2 in. About how much did the trees diameter increase? The trees cross-section area? Q.12 Determine the values of constants a, b, c, and d so that f(x) = ar't ba2+cz+d has a local maximum at the point (0,0) and a local minimum at the point (1,-1). ===All the Best!--
Reid WolffLv2
27 Oct 2019