Limits

Question 0

Horizontal asymptote

Biggest player

Answer 0

X—–> +-$
X^2/X^2—-> coeffs
X^2/X^3—-> 0
X^3/X^2—-> $ no HA

Question 1

Vertical asymptote

Answer 1

Y=#/0
What makes denominator zero
-factor
-solve for x

Question 2

Def of limit

Answer 2

Lim x~>a- f(x)=
lim x~>a+ f(x)=
lim x~>a f(x)=
EXISTS!!

Question 3

Sandwich theorem

Lim x~>0 sin(1/x)

Answer 3

-If top or bottom approaches 0, the function inside goes to 0.
-Sin oscillates from 1~>-1~>1~>-1…
So there is no lim
-1/X goes to $

Question 4

Lim x~>0 [sinx/x]

Answer 4

=1

Question 5

Lim x~>0 [1-cos(x)/x]

Answer 5

=0

Question 6

Discontinuity 4 types

Answer 6

Removable- limit at point isn’t same
Jump- one sided limits r not same
Infinite- @ least 1 limit approaches $
Oscillatory- values near a point vary ————–too much to exist.