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y=(1/c)f(x)
compress the graph by a factor of c
y=f(cx)
compress the graph horizontally by a factor of c
y=f(x/c)
stretch the graph horizontally by a factor of c
y=-f(x)
reflect the graph about the x-axis
y=f(-x)
reflect the graph about the y-axis
(f+g)(x)=
f(x)+g(x)
(f-g)(x)
f(x)-g(x)
(fg) (x)=
f(x)g(x)
(f/g)(x)
f(x)/g(x)
limit
f(x) gets arbitrarily close to L as x gets sufficiently close to a
heaviside function
H(t)= 0 if t<0 1 if t <= 0
a limit exists as
x approaches a iff both the left and right hand limits exist and they are equal
lim{f(x)+g(x)}
limf(x)+limg(x)
lim{f(x)-g(x)}
lim f(x) - lim g(x)
lim cf(x)
c lim f(x)
lim{f(x)g(x)}
[lim f(x)][lim g(x)]
lim[f(x)/g(x)]
{lim f(x)}/{lim g(x)}
lim[f(x)]^n
{lim f(x)}^n
lim c
c
lim x
a
lim x^n
a^n
lim (x)^1/n
a^1/n when n is a positive integer and a> 0 if n is even
lim (f(x))^1/n
(lim f(x))^1/n n is a positive integer and lim f(x)>0 if n is even
direct substitution property
if f is a polynomial or rational function, then the limit f(x)=f(a) as x approaches a also holds for trig functions
lim |x|
0
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