Use the method of cylindrical shells to find the volume V generated by rotating the region bounded by the given curves about y = 8. 64y = x3, y = 0, x = 8

take the logarithm of both sides (the base of the log doesn't matter):

apply the exponent property - this says that :

distribute the log terms on both sides:

group like terms together:

divide through both sides by the coefficient on :

you can do some additional rewriting here using the properties of the logarithm to simplify things if you like:

y = -1

x = 8

hope this !

the cost function, c(x), is the total cost of manufacturing x units of the product. how many units must the company produce and sell if they wish to make a b. if the company produces and sells 2000 units, would they obtain a profit or loss?