prompt answer

for some reason when i post as a comment, i start missing pieces of this so....

a.) jumps
a jump is a gap in the graph, its easy to spot and is usually in the form of a piecewise. to see if there is a jump in the graph, plug in for x. if you dont get the same answers than there is a jump. or if there is a fraction you factor as far as possible, cancel what you can, set bottom equal to 0, and solve for x, if the x value you find at the end still causes the bottom to equal 0, there is a jump

lim
x->2
xx^3-4
x
after plugging in 2, we find that the values are not equal, therefore there is a jump

b.)removable
a removable is easy to spot, its a hole in the graph and it always has a limit. to find a removable: factor, cancel, bottom to 0, x=# is the removable

lim
x->2
x3
factor: yes. (x+3)(x-3)/x-3
cancel:x-3 cancels out
x=3 is a removable

c.)vertical asymptote
once again, the x value at the bottom causes it to equal zero after direct substitution. factor, cancel, set bottom to 0, x is the vertical asypmtote

lim x+6/x-5
x->5
factor: already done
cancel: cannot
bottom to zero
x=5 is a vertical asymptote