Exam 11: Limits and Continuity

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).

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

The solution of (x + 1)( - 1)< 0 is

The solution of - 13x + 6 ≤ 0 is

An open box is formed by cutting a square piece out of each corner of a 8-inch by 12-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: Find

The solution of + 6x + 1 < 0 is

Let f(x)= .The only value(s)of x for which f is discontinuous is (are)

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

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

Solve the inequality: + x ≥ 2.

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

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

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

Solve: < 0

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

f(x)= Find (a) f(x) (b) f(x) (c) f(x)

=

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