Limits From Graph and Table
Limits Analytically
Asymptotes
100
Evaluate the following:
lim_(x->1^+)=
lim_(x->1^+)=-4
100
lim_(x->2) 2x^3-3x-14
-4
100
Find the horizontal asymptote of the following.
f(x)={x+10}/{x^2-x+14)
y=0
200
lim_(x->3^-)=
lim_(x->3^+)=
lim_(x->3^-)=10
lim_(x->3^+)=10
200
lim_(x->-3)=x^3+2x^2+12
3
200
Evaluate the limit.
lim_(x->4^-) {x+3}/{x-4}
-oo
300
lim_(x->-4^-)=
3
300
lim_(x->-3) {x^2+5x+6}/{x^2-x-12}
1/7
300
Evaluate the limit.
lim_(x->oo){7x-4x^2+10}/{8-10x-2x^2}
2
400
lim_(x->3)=
lim_(x->3)=-2
400
lim_(x->6) {sqrt(x+3)-3}/(x-6)
1/6
400
Find the vertical asymptote.
f(x)={x^2-2x+1}/{x^2+3x-4}
x=-4
500
lim_(x->-1^-)=
lim_(x->-1^+)=
lim_(x->-1)=
lim_(x->-1^-)=0
lim_(x->-1^+)=-2
lim_(x->-1) = DNE
500
lim_(x->3) {1/4-1/(x+1)}/(x-3)
1/16
500
Find all horizontal and vertical asymptotes of the following.
f(x)={6x^2-5x-1}/{x^2-1}
Horizontal asymptote: y=6
Vertical asymptote: x=-1