Find the arc length of a curve defined by trigonometric

The graphs of x 8 y f x solid and y g x dashed are shown the graph is not drawn to scale Region One B A a The intersection points are A 8 4 B 8 7 and C 1 5 Suppose Region One is revolved around the x axis Using the method of washers the volume can be computed by evaluating the integral

Problem 1 10 points At a certain moment the dimensions of a cylinder are changing as follows The radius is decreasing at a rate of 1 cm s The height is increasing at a rate ofcm s 5 The volume is decreasing at a rate of 87 cm s The surface area is decreasing at a rate of 44 3 cm s Find all the possible values of the radius and the height at this moment

Find the critical numbers of the function Enter your answers as a comma separated list If an answer does not exist enter DNE f x 2x 3x 12x

3 4 pts Find the directions in which the function increases and decreases most rapidly AND the derivatives of the function in those directions g x y a xe z P 1 42

Find the antiderivatives for dy dx 800x6 y C

Find the most general antiderivative of the function Answer F x f x 8e 6 sec x You can use C for any needed constant in your answer

0 Graphy Log x 4 3 2

A circular swimming pool has a diameter of 20 m The circular side of the pool is 4 m high and the depth of the water is 3 5 m The acceleration due to gravity is 9 8 m s and the density of water is 1000 kg m How much work in Joules is required to a pump all of the water over the side b pump all of the water out of an outlet 2 m over the side

cos n Find the limit of the sequence an 3n

2 Find two numbers whose difference is fifteen such that the square of the first number plus twice the square of the second number is a minimum Don t forget to explain which of the two numbers that you find gets squared and which number gets squared then doubled