L'Hospital's Rule
AP Calculus BC · Flashcards
AP CALCULUS BC · FLASHCARDS
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QUESTION
Find
lim
x
→
∞
x
2
e
x
\lim_{{x \to \infty}} \frac{x^2}{e^x}
lim
x
→
∞
e
x
x
2
using L'Hospital's Rule.
QUESTION
Is L'Hospital's Rule applicable to
lim
x
→
2
x
2
−
4
x
−
2
\lim_{{x \to 2}} \frac{x^2 - 4}{x - 2}
lim
x
→
2
x
−
2
x
2
−
4
?
QUESTION
Find
lim
x
→
0
tan
x
x
\lim_{{x \to 0}} \frac{\tan x}{x}
lim
x
→
0
x
t
a
n
x
using L'Hospital's Rule.
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ANSWER
1.
d
d
x
(
tan
x
)
=
sec
2
x
\frac{d}{dx}(\tan x) = \sec^2 x
d
x
d
(
tan
x
)
=
sec
2
x
and
d
d
x
(
x
)
=
1
\frac{d}{dx}(x) = 1
d
x
d
(
x
)
=
1
, so
1
1
=
1
\frac{1}{1} = 1
1
1
=
1
.
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