Limits
Types of Discontinuities
Functions Continuous on Their Domains
Asymptotes
Derivatives
100
lim 5 x->2
5
100
What type of discontinuity is the function f(x)=(x^2-x-2)/x-2
removable discontinuity
100
On what domain are polynomial functions continuous?
(-infinity, infinity)
100
Given the function, f(x)=(3e^-x)+2 give equation(s) of any horizontal asymptotes
y=2
100
Find the derivative of f(x)=x^2 at x=3
f'(3)=6
200
lim 12345 x->4
12345
200
What type of discontinuity is the function f(x)=1/(x+1)
infinite discontinuity
200
On what domain are inverse sin and cos functions continuous?
[-1,1]
200
Given the function, give the equations of any horizontal asymptotes f(x)=(3x^3-1)/x^4
y=0
200
Given f(x)=x^2 -1 find f'(a) if a=-3
-6
300
lim ((2+x)^3-8)/x x->0
12
300
What type of discontinuity is the function f(x)={3x+1, x≥0 2x-1, x<0
jump discontinuity
300
On what domain are odd root functions continuous?
(-infinity, infinity)
300
Given the function, determine the equations of any vertical asymptotes f(x)=(x-6)/((x+5)(x-6))
x=-5
300
Given f(x)=x^2 +2x-1 find f'(-1)
0
400
lim (x-1)/(x^2-1) x->1
1/2
400
What type of discontinuity is the function f(x)=x/(x+5)
infinite discontinuity
400
On what domain is the function "y=logx-2" continuous?
(2, infinity)
400
Given the function, give equations of any horizontal asymptotes f(x)=(1-x=x^2-4x^3)/(5x^2+2x-1)
no horizontal asymptotes
400
Given f(x)=x^2 -4x find f'(-2)
-8
500
lim (3sin4x)/sin3x x->0
0
500
What types of discontinuities does the function have f(x)=x/(x(x+5))
infinite at x=-5 removable at x=0
500
On what domain is the function f(x)= 1/x continuous?
(-infinity, 0)U(0, infinity)
500
Given the function, determine any horizontal asymptotes y=cos(5/x)
y=1
500
Given f(x)=1/x find f'(1)
-1
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