Function Graph
f(x) = sin(x)/x
Controls
Limit Analysis
Left-hand limit L⁻
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Right-hand limit L⁺
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Limit exists?
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Limit value L
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f(a) value
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Continuous at a?
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Discontinuity type
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Current ε
0.50
Required δ estimate
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Preset Scenarios
Limit exists iff:
L⁻ = L⁺ = L
Continuity at a:
1. f(a) is defined
2. limx→a f(x) exists
3. lim = f(a)
Discontinuity types:
Removable — limit exists, f(a) ≠ L
Jump — L⁻ ≠ L⁺, both finite
Infinite — limit is ±∞
L⁻ = L⁺ = L
Continuity at a:
1. f(a) is defined
2. limx→a f(x) exists
3. lim = f(a)
Discontinuity types:
Removable — limit exists, f(a) ≠ L
Jump — L⁻ ≠ L⁺, both finite
Infinite — limit is ±∞