Exam 11: Limits and Continuity

An open box is formed by cutting a square piece out of each corner of a 12-inch by 10-inch piece of metal.If each side of the squares cut out is x inches long,the volume of the box is given by This problem only makes sense when this volume is positive.Find the values of x for which the volume is positive.

Find: .If the limit does not exist,so state or use the symbol ∞ or if appropriate.

Find: .If the limit does not exist,so state or use the symbol ∞ or -∞ if appropriate.

The greatest integer function in mathematics (denoted f(x)= )is used every day by cashiers making change for customers.This function tells the amount of paper money for each amount of change owed.(For example,if the customer is owed $1.25 in change,he would get $1 in paper money,thus = 1).By considering , , , ,and ,determine .

Solve the inequality: ≤ 0.

A container manufacturer will make an open box by cutting a 3-inch square from each corner of a square sheet of aluminum and then turning up the sides.The box is to contain at least 300 .Find the dimensions of the smallest sheet of aluminum that can be used.

Find: .If the limit does not exist,so state or use the symbol ∞ or -∞ if appropriate.

Find: .If the limit does not exist,so state or use the symbol ∞ or -∞ if appropriate.

By looking at the graph below,state whether the function f(x)is continuous or discontinuous at x= -1.

The yearly sales y of a certain company (in thousands of dollars)is related to the amount that company spends on advertising,x (in thousands of dollars),according to the equation y(x)= .Find y(x)and discuss what this means to the company.

The greatest integer function in mathematics (denoted f(x)= )is used every day by cashiers making change for customers.This function tells the amount of paper money for each amount of change owed.(For example,if the customer is owed $1.25 in change,he would get $1 in paper money,thus = 1).By considering , , , ,and ,determine .

The cost of purifying water is given by C = - 2000 where C is the cost in dollars and p is the percent of impurities left in the water after purification.Graph this function on your graphing calculator and explore the graph as the percent of impurities gets very small.Compare the cost of increasing the purity of the rate from 5% to 6% with the cost of increasing the impurity from 50% to 51%.What does this mean?

=

The demand function for a certain product is given by: p = ,where p is the price and q is the quantity demanded. (a)Find the values of q for which p > 0. (b)Find the values of q for which p < 0. (c)What do the results of (a)and (b)mean and why does this make sense?

Find the value(s)of x for which f(x)= + 2x - 5 is discontinuous.

Find the value(s)of x for which f(x)= is discontinuous.

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Find: g(x)

The demand function for a certain product is given by p(x)= where p is the price in dollars and x is the quantity sold.Graph this on your graphing calculator in the window × .Use the TRACE function to find p(x).Describe in words what is happening to the graph and what this means about the demand function.

The cost of purifying water is given by C = - 3750 where C is the cost in dollars and p is the percent of impurities left in the water after purification.Find .