Determining Limits Using Algebraic Manipulation
AP Calculus BC · Flashcards · Recall
AP CALCULUS BC · FLASHCARDS
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QUESTION
What algebraic technique is most appropriate for
lim
x
→
a
u
(
x
)
−
v
(
x
)
w
(
x
)
\lim_{x\to a}\frac{\sqrt{u(x)}-\sqrt{v(x)}}{w(x)}
lim
x
→
a
w
(
x
)
u
(
x
)
−
v
(
x
)
when direct substitution gives
0
0
\frac{0}{0}
0
0
?
QUESTION
What is the standard limit value
lim
u
→
0
1
−
cos
u
u
2
\lim_{u\to 0}\frac{1-\cos u}{u^2}
lim
u
→
0
u
2
1
−
c
o
s
u
used in algebraic manipulation?
QUESTION
What algebraic technique is most appropriate when
lim
x
→
a
f
(
x
)
g
(
x
)
\lim_{x\to a}\frac{f(x)}{g(x)}
lim
x
→
a
g
(
x
)
f
(
x
)
gives
0
0
\frac{0}{0}
0
0
and
f
,
g
f,g
f
,
g
are polynomials?
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ANSWER
Factor numerator and denominator, then cancel the common factor. This eliminates the indeterminate form
0
0
\frac{0}{0}
0
0
.
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