Exam 11: Limits and Continuity

Find: Find

A television repair technician charges $100 for the first hour of work at your house and $50 for every hour (or fraction thereof)afterwards.The function for what the visit will cost you is given by: f(x)= (a)Find f(x) (b)Find f(x) (c)Find f(x)

The volume of helium in a spherical balloon (in cubic centimeters)as a function of the radius,r,in centimeters,is given by V(r)= π .Find V(r).

An open box is formed by cutting a square piece out of each corner of a 8-inch by 8-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.

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

Solve: < 0

The revenue R for a product is given by R(x)= 750x - where x is the number of units sold.Graph this function on your graphing calculator in several different viewing rectangles.Discuss whether you think this function is continuous or not.

Find where f(x)=

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

Find: lim 15 x→8

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 where f(x)=

Find:

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?

Consider the graph of f(x) Determine the following limits: (a) f(x)(d)f(3) (b) f(x)(e) f(x) (c) f(x)(f) f(x)

Find: lim ( - 4x + 3) x→3

Suppose that the rent for an apartment in a city with rent control is $480 per month.Show that the rent function R(t)= 480 is continuous at t = 7.

Let f(x)= Find all points where this function f(x)is not continuous.

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

Find: