Exam 11: Limits and Continuity

Solve: ≥ 0

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 revenue function for a certain product is given by R(x)= 500x - .Find R(x).

Solve: - 2x - 3 < 0

If f(x)= ,find f(x).Hint: Sketch the graph of f.

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

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 profit function for a product is given by P(x)= 37x + - 6300.Determine for what values of x the profit is positive.

Solve: (x - 1)(x + 2)(x - 3)≤ 0

The solution of < 0 is

The length of a material increases as it is heated up according to the equation The rate at which the length is increasing is given by: Calculate this limit.

Solve: < 0

Find: 7.If the limit does not exist,so state or use the symbol ∞ or -∞ if appropriate.

The profit function for a product is given by P(x)= 35x + - 4950.Determine for what values of x the profit is positive.

Find:

Solve: (x - (x + 4)> 0

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.

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

The cost of purifying water is given by C = - 5500 where C is the cost in dollars and p is the percent of impurities left in the water after purification.Find .

If f(x)= ,then F(x)=