Course
Calculus I — Practice Problems with Worked Solutions
Single-variable calculus for engineers. 361 problems across 21 skills, each solved step by step and verified by a computer algebra system.
- 361
- problems
- 21
- skills
- 6
- units
- 24
- formulas
Limits & Continuity
- Evaluating LimitsSubstitute when you can; factor and cancel when you get 0/0.26 worked problems
- One-Sided LimitsApproach from the left or right. The branch you follow matters.16 worked problems
- Limits at InfinityHighest powers decide the long-run behavior.16 worked problems
- ContinuityThe limit, the function value, and both sides must meet.16 worked problems
Derivative Foundations
- Derivative from First PrinciplesSlope emerges from a limit of secant lines.16 worked problems
- Power RuleThe workhorse. Bring the exponent down, step it down by one.26 worked problems
- Trigonometric DerivativesSine, cosine, and tangent have their own derivative rhythm.16 worked problems
- Exponential & Log Derivativese^x repeats itself; ln x turns multiplication into structure.16 worked problems
Differentiation Techniques
- Product RuleTwo functions multiplied — g'h + gh'. Mind the classic trap.16 worked problems
- Quotient Ruleg over h. Low d-high minus high d-low, over the square of what's below.16 worked problems
- Chain RuleFunctions inside functions. Never forget the inner derivative.17 worked problems
- Implicit DifferentiationWhen y will not isolate nicely, differentiate the relationship.16 worked problems
Applications of Derivatives
Integration
- AntiderivativesRun the power rule in reverse. Don't forget the + C.18 worked problems
- Definite IntegralsAntiderivative, then evaluate top minus bottom.16 worked problems
- Fundamental Theorem of CalculusDifferentiation and integration are inverse operations.16 worked problems
- u-SubstitutionReverse the chain rule by naming the inner expression.18 worked problems