Exam 11: Limits and Continuity

Find: Find

The cost C of producing x units of a certain product is given by Find C(x)and discuss what this means.

The revenue R for a product is given by R(x)= 2500x - where x is the number of units sold.Is this function continuous for x = 50?

Use the definition of continuity to show that f(x)= is continuous at x = -5.

Why can we say that f(x)= - 9 + 7 - 5 - 8x + 1 is continuous on (-∞,∞)?

Consider the graph of f(x) Determine the following limits: (a) f(x)(d)f(-2)(g) f(x) (b) f(x)(e) f(x)(h)f(1) (c) f(x)(f) f(x)

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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.Find p(x).

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

The solution of (x + 2)(x + 4)(2x - 3)< 0 is

Solve the inequality: < 0.

Solve: - x - 6 ≥ 0

The revenue R for a product is given by R(x)= 2500x - where x is the number of units sold.Is this function continuous for x = 20?

Use the definition of continuity to show that f(x)= - 3x + 1 is continuous at x = 2.

The profit function for a product is given by P(x)= 28x + - 960.Determine for what values of x the profit is positive.

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.Find .

The profit function for a certain business is given by: P(x)= 225x - - 800.Graph this function on your graphing calculator and use the evaluation function to determine P(x)using the rule about the limit of a polynomial function.

Solve the inequality: > 0.

Find the following limit.If it is +∞ or -∞ or does not exist,then say so.

Find: