Interactive Real Analysis
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Real Analysis
1. Sets and Relations
2. Infinity and Induction
3. Sequences of Numbers
4. Series of Numbers
5. Topology
6. Limits, Continuity, and Differentiation
6.1. Limits
6.2. Continuous Functions
6.3. Discontinuous Functions
6.4. Topology and Continuity
6.5. Differentiable Functions
6.6. A Function Primer
7. The Integral
8. Sequences of Functions
9. Historical Tidbits
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6.5. Differentiable Functions
Examples 6.5.16(a):
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L'Hospital's Rule applies directly in this case. If
g(x) = sin(x)
and
f(x) = x
, then
g'(x) = cos(x)
and
f'(x) = 1
. Hence, by l'Hospital's rule, we have:
= cos(0) / 1 = 1
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