Exam 11: Limits and Continuity

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

Solve: ≥ 0

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

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?

=

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 .Graph V(r)in the standard viewing rectangle, × and use TRACE to estimate V(r).

By looking at the graph,give the following limits. (a) f(x) (b) f(x) (c) f(x)

If f(x)= 3x - 7,then =

By looking at the graph,give the following limits. (a) f(x) (b) f(x)

The rate of change of productivity p (in number of units produced per hour)increases with time on the job by the function p = .Find p.

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).

Let f(x)= Find all points of discontinuity for this function.

Solve the inequality: < 0.

A lawyer charges $300 for the first hour of work at your house and $100 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 cost C of processing exhaust gases so that you remove all but x percent of the pollutants is given by Find the values of x for which C < 0.Discuss the meaning of the results.

If the profit function for a certain business is given by: P(x)= 225x - - 800,use the rule about the limit of a polynomial function to determine P(x).

Find: $\lim_{x \rightarrow 5}$ $\frac{x^{2}}{h}$

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

Find where f(x)= + 3x + 5