1.5-1.7 Flashcards
(49 cards)
properties of limits only true if
approaching same number
lim as x–> c of (b*f(x))=
b*L
lim as x–> c of f(x)+g(x)=
L+K
lim as x–> c of f(x)*g(x)=
L*K
0/1 or 1/0
cannot divide by 0
lim as x–> c of f(x)/g(x)=
L/K
lim as x–> c of f(x)^n=
L^n
lim as x–> c of f(g(x))=
f(lim as x–> c of g(x)) as long as…
-the g(x) limit exists
-f(x) is continuous
if when using our properties of limits one limit DNE
find from both directions!
- if same from both sides the limit exists!
lim from left=
lim from below
lim from right=
lim from above
a limit asks
what is my y-value approaching?
lim as x–> c of b=
b as b is a horizontal line
lim as x–> c of x=
c as x is a line with a slope of 1
lim as x–> c of x^n=
c^n
if when solving a limit algebraically you get 0/0
do more!
do more means…
- factor and cancel
- multiply by conjugate
- get rid of fraction
conjugate of (x+5)-1
(x+5)+1
remember when multiplying to
FOIL
do not drop off
limit statement!
to get rid of fraction
- get common denominator ad combine
- multiply by reciprocal
- plug in
if lim of g(x+1)
add the 1 to the x-value approaching
squeeze theorem
if h(x)<f(x)<g(x) on an interval containing c and
lim x–>c h(x) = L= lim x–>c g(x) then
lim x–> c f(x) = L
lim x –> 0 sinx/x
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