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limit
Limits and Continuity
Understand what a graph approaches and when a function has no break.
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Course outline · Derivative Dimension
Calculus I
Limits, continuity, derivative rules, applications, optimization, antiderivatives, and basic integrals.
This page is a topic roadmap with links to existing practice. Full course videos and connected course progress are not available. Read complete written lessons in Learn.
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17
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3
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0
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3
2
limit-laws
Limit Laws
Use algebraic rules to evaluate limits efficiently.
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3
one-sided
One-Sided Limits
Compare approaching from the left and right.
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4
asymptote
Infinite Limits
Recognize vertical asymptotes and unbounded behavior.
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5
tangent
Definition of Derivative
Build the derivative from average rate of change and tangent slope.
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6
rule-card
Derivative Rules
Differentiate powers, sums, constants, and basic functions.
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7
rule-card
Product and Quotient Rule
Differentiate products and ratios without losing terms.
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8
chain
Chain Rule
Differentiate composite functions one layer at a time.
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9
implicit
Implicit Differentiation
Differentiate equations where y is mixed with x.
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10
rates
Related Rates
Connect changing quantities with equations and derivatives.
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11
tangent
Linear Approximation
Use tangent lines to estimate nearby values.
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12
slope-sign
Increasing and Decreasing Functions
Use derivative signs to identify where functions rise or fall.
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13
concavity
Concavity and Inflection Points
Use second derivative intuition to see bending behavior.
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14
peak
Optimization
Use derivatives to maximize or minimize real quantities.
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15
reverse
Antiderivatives
Reverse derivative rules to find original functions.
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16
area
Area Under a Curve
Connect accumulated area to integral intuition.
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17
integral
Basic Definite Integrals
Evaluate simple accumulated change with bounds.
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