New Hampshire Calculus: Limits, Derivatives, and Integrals
Calculus is one of the most important math courses New Hampshire high school students will take. It builds directly on algebra, geometry, and pre-calculus skills to introduce new concepts like limits, derivatives, and integrals. StudyPug covers every major Calculus topic with video lessons and practice problems aligned to NH Mathematics Model Competencies.
Limits and Continuity
Calculus begins with understanding limits — what a function approaches as inputs get close to a value. New Hampshire students learn to evaluate limits graphically, numerically, and using substitution. From there, they study continuity at a point, identify types of discontinuities, and explore limits at infinity to describe end behavior of functions.
Derivatives and Differentiation Rules
The derivative is the foundation of differential calculus. Students learn to interpret the derivative as a rate of change and the slope of a tangent line. StudyPug covers all key differentiation rules:
- Power rule, product rule, quotient rule, and chain rule
- Derivatives of trigonometric, exponential, and logarithmic functions
- Implicit differentiation for functions not written explicitly
- Equations of tangent lines and linear approximation
Applications of Derivatives
Once students understand how to find derivatives, they apply them to real problems. Topics include finding critical points, local maxima and minima, and solving optimization problems. Students also analyze increasing and decreasing behavior, concavity, and use curve sketching. Related rates problems and applications to velocity and acceleration connect calculus to real-world contexts.
Integration and Antiderivatives
The second half of Calculus focuses on integrals. Students start by finding antiderivatives of basic functions and using initial conditions. They then learn to approximate definite integrals using left, right, and midpoint Riemann sums before applying the Fundamental Theorem of Calculus (FTC) to evaluate integrals exactly.
- Substitution method for evaluating integrals
- Area under curves and between curves
- Displacement and distance from velocity functions
- Average value of a function over an interval
How StudyPug Helps New Hampshire Calculus Students
StudyPug provides video lessons and practice problems for every Calculus topic. Each lesson is 5-15 minutes long and broken into short segments students can pause and replay. New Hampshire students can use StudyPug on any device — computer, tablet, or phone — to get help with homework, prepare for tests, or review topics they found difficult in class.
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