1. for each of the following, find

a: lim x-->a- f(x)

b: lim x-->a+ f(x)

c: lim x-->a f(x)

show your work/ justify your answers:

A: f(x)={3x+1 x<2

{8 x=2 a=2

{x^2 +3 x>2

a:

b:

c:

B: f(x)=3-x/|x-3| a=3

a:

b:

c:

C: f(x)=[sqrt(3+x)-sqrt(3)]/x a=0

a:

b:

c:

D: f(x)={sinx/2 x<2pi>

{x^2/pi x> and equals 2pi/3 a=2pi/3

a:

b:

c:

2.Sketch a graph of each function

A: a function that is continuous everywhere except at x=4. At x=4 the function is continuous from the right but not continuous from the left

B: a function that has a removable continuous at x=-2 and an infinite discontinuity at x=3, but is continuous elsewhere

C:a function such that lim x--->infinity f(x)=-2, lim x--->negative infinity f(x)=3, f(2)=1, f(-2)=5, lim x---> -1f(x)=infinity

D: graph f(x)={sqrt(x-2) x> and equals 3

{|x-1| x<3 and determine if f(x) is continuous at 3. Use limits to justify your answer