L'Hospital's Rule
AP Calculus AB · Flashcards
AP CALCULUS AB · FLASHCARDS
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QUESTION
Identify the indeterminate form:
lim
x
→
∞
x
2
x
2
+
x
\lim_{x \to \infty} \frac{x^2}{x^2 + x}
lim
x
→
∞
x
2
+
x
x
2
.
QUESTION
Find the limit:
lim
x
→
∞
x
x
2
+
1
\lim_{x \to \infty} \frac{x}{x^2 + 1}
lim
x
→
∞
x
2
+
1
x
using L'Hospital's Rule.
QUESTION
Find the limit:
lim
x
→
∞
3
x
2
2
x
2
+
5
\lim_{x \to \infty} \frac{3x^2}{2x^2 + 5}
lim
x
→
∞
2
x
2
+
5
3
x
2
using L'Hospital's Rule.
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ANSWER
3
2
\frac{3}{2}
2
3
. After applying L'Hospital's Rule:
lim
x
→
∞
6
x
4
x
=
6
4
=
3
2
\lim_{x \to \infty} \frac{6x}{4x} = \frac{6}{4} = \frac{3}{2}
lim
x
→
∞
4
x
6
x
=
4
6
=
2
3
.
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