Determining Limits Using Algebraic Manipulation
AP Calculus BC · Flashcards
AP CALCULUS BC · FLASHCARDS
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QUESTION
What is
lim
x
→
0
x
1
+
x
−
1
\lim_{x\to 0}\frac{x}{\sqrt{1+x}-1}
lim
x
→
0
1
+
x
−
1
x
after rationalizing?
QUESTION
What is
lim
x
→
0
1
x
+
1
−
1
x
\lim_{x\to 0}\frac{\frac{1}{x+1}-1}{x}
lim
x
→
0
x
x
+
1
1
−
1
?
QUESTION
What is
lim
x
→
1
x
−
1
x
−
1
\lim_{x\to 1}\frac{x-1}{\sqrt{x}-1}
lim
x
→
1
x
−
1
x
−
1
?
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ANSWER
2
2
2
. Factor numerator:
(
x
−
1
)
(
x
+
1
)
x
−
1
=
x
+
1
\frac{(\sqrt{x}-1)(\sqrt{x}+1)}{\sqrt{x}-1} = \sqrt{x}+1
x
−
1
(
x
−
1
)
(
x
+
1
)
=
x
+
1
.
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