Limits
Asymptotes
Continuity and Discontinuities
Intermediate Value Theorem
100
Lim x->3 (5x²-8x-13)/(x²-5)
2
100
Find the domain and vertical asymptotes of the following: y= (x²+3x+1)/(4x²-9)
Domain: x cannot equal 3/2, -3/2 VA: x=3/2 x=-3/2
100
Discuss the continuity of each function by graphing y=(1/x)
Non-removable discontinuity at x=0
100
Use Intermediate Value Theorem to solve: f(x)= (x³+x-1)
.68 and .6823
200
lim x->2 (3x²-x-10)/(x²-4)
11/4
200
DOUBLE JEOPARDY! Find the domain and horizontal asymptotes: y= (x+3)/(x²+9)
Domain: All real numbers Horizontal: y=0
200
Discuss the continuity of each function by graphing y=(x²-1)/(x-1)
Removable discontinuity at x=1
200
Solve using Intermediate Value Theorem g(t)= 2cos(t)-3t
.56, .5636
300
lim x->(π/2) (tan2x)/([x-(π/2)]
2
300
Find the domain and the vertical and horizontal asymptotes: y= (x²-x-2)/(x-2)
Domain: x cannot equal 2 VA: x=2 HA: None
300
Discuss the continuity of each function by graphing y=sinx
Continuous on entire real line
300
Use Intermediate Value Theorem to verify c applies on interval. f(x)= x²+x-1 Interval: [0,5] f(c)=11
f(3)=11
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