vertical asymptotes
and holes
and holes
limit notations
pascal's triangle
100
Hole: x=1
V.A.: x=-3
100
H(x)=(-3x4-x2+x)
/(x3+4x+4)
left= lim f(x)= infinity when x-> - infinity
right= lim f(x)= - infinity when x-> infinity
100
What is the coefficient of the term containing x2 when the expression (x+4)4 is expanded?
6
200
Hole: x=2
V.A.: X=3
200
P(x)=2x3+4x-1/
6x3-x2+4
left: lim f(x)= 1/3 when x-> - infinity
right: lim f(x)= -1/3 when x -> infinity
200
What is the coefficient of the term containing y3 when the expression (x-3) is expanded?
4
300
h(x)=(x+4)(x-3)2/(x-3)(x+5)
Hole at x=3
V.A. at x=-5
300
g(x)= 5x2-8x+9 /
2x3+x-1
left: lim f(x) = 0 when x-> - infinity
right: lim f(x)= 0 when x-> infinity
300
expand (x+5)3
1(x)3 + 3(x)2(5) + 3(x)(5)2 + 1(5)3
400
g(x)=x2-1/x2+3x+2
Hole at x=-1
V.A at x=-2
400
f(x) = (x-1)(x+3) /
(x-2)
left: lim f(x)= infinity when x-> - infinity
right: lim f(x)= - infinity when x-> infinity
400
expand (x-2)5
1(x)5 + 5(x)4(-2) + 10(x)3(-2)2 + 10(x)2(-2)3 + 5(x)(-2)4 + 1(-2)5
500
f(x)=(x-3)2/x2-5x+6
V.A. at x=2
Hole at x=3
500
g(x)= (x-2)(x+4)/
(x-2)(x-3)
left: lim g(x)= -6 when x-> 2
right: lim g(x)= -6 when x->2
500
expand (x-5)6
1(x)6 + 6(x)5(-5) + 15(x)4(-5)2 + 20(x)3(-5)3 + 15(x)2(-5)4 + 6(x)(-5)5 + 1(x)6