1. Find the derivatives of the following functions: A. f(x) = sin(x) cos(x) B. g(x) =...

  

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1. Find the derivatives of the following functions: A. f(x) = sin(x) cos(x) B. g(x) = x sin(x) 2. Find the derivative of the function (2) = sin() and compute h' (2). 3. Consider the curve described by the equation 2y - = 4y. Verify that the point (4, -2) lies on this curve, and find y at that point. 4. Water is being drained from a container which has the shape of an inverted right circular cone. The container has a radius of 7 inches at the top and a height of 9 inches. At the instant when the water in the container is 8 inches deep, the surface level is falling at a rate of 1.4 in. Find the rate at which the water is being drained from the container at the same instant. Exact answers only (i.e.) make sure your answer has in it!) Hint: Draw a picture to help you get started, and remember similar triangles. 5. A man walks along a straight path at a speed of 5. A searchlight is located on the ground 20 feet from the path and is kept focused on the man. At what rate is the searchlight rotating when the man is 15 feet from the point on the path closest to the searchlight? (Angle is measured in radians for the units). 20 (Description: A man is drawn on a straight path labeled a. A segment of length 20 is drawn at a right angle from the straight path. Another segment connects the segment drawn at a right angle to the straight path where the man is, the angle is labeled (.) Bonus Problem (3 pts): Find the linear approximation for y=for a = 125. Then use to estimate the following: a) 126 b) 125.50 1. Find the derivatives of the following functions: A. f(x) = sin(x) cos(x) B. g(x) = x sin(x) 2. Find the derivative of the function (2) = sin() and compute h' (2). 3. Consider the curve described by the equation 2y - = 4y. Verify that the point (4, -2) lies on this curve, and find y at that point. 4. Water is being drained from a container which has the shape of an inverted right circular cone. The container has a radius of 7 inches at the top and a height of 9 inches. At the instant when the water in the container is 8 inches deep, the surface level is falling at a rate of 1.4 in. Find the rate at which the water is being drained from the container at the same instant. Exact answers only (i.e.) make sure your answer has in it!) Hint: Draw a picture to help you get started, and remember similar triangles. 5. A man walks along a straight path at a speed of 5. A searchlight is located on the ground 20 feet from the path and is kept focused on the man. At what rate is the searchlight rotating when the man is 15 feet from the point on the path closest to the searchlight? (Angle is measured in radians for the units). 20 (Description: A man is drawn on a straight path labeled a. A segment of length 20 is drawn at a right angle from the straight path. Another segment connects the segment drawn at a right angle to the straight path where the man is, the angle is labeled (.) Bonus Problem (3 pts): Find the linear approximation for y=for a = 125. Then use to estimate the following: a) 126 b) 125.50