CALCULUS COMPLETE GUIDE: Step-by-Step Solutions
AUTHOR: Gracy
TABLE OF CONTENT
• Limits and Continuity
• Differentiation
• Integration Techniques
• Applications of Differentiation
• Applications of Integration
• Common Exam Problems
1. Limits and Continuity
Definition:
The limit of a function f(x) as x approaches a value a is the value f(x) gets closer to as x
approaches a.
Example:
Evaluate: lim (x -> 2) of (3x^2 + 5)
Solution:
3*(2^2) + 5 = 12 + 5 = 17
2. Differentiation
Rule:
d/dx [x^n] = n * x^(n-1)
Example:
Differentiate f(x) = 5x^3 + 2x
Solution:
F’(x) = 15x^2 + 2
3. Integration Techniques
Rule:
Integral of x^n dx = x^(n+1)/(n+1) + C (n ≠ -1)
AUTHOR: Gracy
TABLE OF CONTENT
• Limits and Continuity
• Differentiation
• Integration Techniques
• Applications of Differentiation
• Applications of Integration
• Common Exam Problems
1. Limits and Continuity
Definition:
The limit of a function f(x) as x approaches a value a is the value f(x) gets closer to as x
approaches a.
Example:
Evaluate: lim (x -> 2) of (3x^2 + 5)
Solution:
3*(2^2) + 5 = 12 + 5 = 17
2. Differentiation
Rule:
d/dx [x^n] = n * x^(n-1)
Example:
Differentiate f(x) = 5x^3 + 2x
Solution:
F’(x) = 15x^2 + 2
3. Integration Techniques
Rule:
Integral of x^n dx = x^(n+1)/(n+1) + C (n ≠ -1)
