USTET Mathematics — Calculus — Limits, Derivatives & IntegralsConcept Map
University of Santo Tomas loves to test Calculus — Limits, Derivatives & Integrals through questions that span multiple sub-topics in one item. A concept map helps you see those cross-links in advance. This page will show the full Calculus — Limits, Derivatives & Integrals concept map for USTET Mathematics once content generation completes.
Exam context
On the USTET 2026, the Mathematics subtest carries a "Core section" weight in University of Santo Tomas's pattern. Calculus — Limits, Derivatives & Integrals lands at position 9th out of 9 in the standard review order. Target score is Competitive overall score, and roughly a meaningful share of items come from Mathematics on a typical USTET paper.
Calculus — Limits, Derivatives & Integrals - Concept map
Central Concept
Calculus
Related Concepts
Concept
Limits
Sub Concepts
- Definition of limits
- Limit theorems
- Evaluating limits
- Indeterminate forms
- Applications in continuity
Relationship To Central
Foundation of calculus - describes behavior of functions as input approaches a value
Concept
Derivatives
Sub Concepts
- Definition using limits
- Power rule
- Product rule
- Quotient rule
- Chain rule
- Applications in optimization
Relationship To Central
Measures instantaneous rate of change using limits
Concept
Integrals
Sub Concepts
- Definite integrals
- Indefinite integrals
- Fundamental Theorem of Calculus
- Basic integration rules
- Applications in area and volume
Relationship To Central
Reverse process of differentiation - finds area under curves
Concept
Functions
Sub Concepts
- Polynomial functions
- Rational functions
- Trigonometric functions
- Exponential functions
- Logarithmic functions
Relationship To Central
Mathematical objects that limits, derivatives, and integrals operate on
Concept Connections
To
Derivatives
From
Limits
Strength
strong
Relationship
Derivatives are defined using limits to find instantaneous rate of change
To
Integrals
From
Derivatives
Strength
strong
Relationship
Integration is the reverse process of differentiation (antiderivative)
To
Integrals
From
Limits
Strength
strong
Relationship
Definite integrals are defined as limits of Riemann sums
To
Derivatives
From
Fundamental Theorem of Calculus
Strength
strong
Relationship
FTC Part 1 shows that derivatives undo integrals
To
Integrals
From
Fundamental Theorem of Calculus
Strength
strong
Relationship
FTC Part 2 provides method for evaluating definite integrals
To
Derivative Rules
From
Limit Theorems
Strength
moderate
Relationship
Many derivative rules are derived from limit theorems
To
Integration Rules
From
Power Rule
Strength
strong
Relationship
Integration of x^n reverses the power rule for derivatives
To
Integration by Parts
From
Product Rule
Strength
moderate
Relationship
Integration by parts is derived from the product rule
To
Substitution Method
From
Chain Rule
Strength
moderate
Relationship
U-substitution in integration reverses the chain rule
To
Limits
From
Continuity
Strength
strong
Relationship
A function is continuous if its limit equals its function value
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