Introductory Calculus for Utah High School Students
Introductory Calculus is one of the most important math courses Utah high school students will take. It builds the foundation for college-level mathematics, engineering, physics, and more. StudyPug's video lessons cover every topic in the course, from evaluating basic limits to calculating the area between curves, all aligned to Utah Core Standards Math.
Limits and Continuity
The course begins with understanding limits graphically and numerically. Students learn to evaluate limits using substitution, determine continuity at a point, identify types of discontinuities, and describe end behavior by finding limits at infinity. These concepts form the foundation of all calculus that follows.
Derivatives
Students learn the derivative as a rate of change and the slope of a tangent line. Key differentiation rules include the power rule, product rule, quotient rule, and chain rule. The course also covers derivatives of trigonometric, exponential, and logarithmic functions, as well as implicit differentiation. Applications include finding tangent line equations, linear approximation, critical points, optimization, curve sketching, and solving related rates and motion problems.
Integrals
The integral unit introduces antiderivatives and initial conditions, Riemann sums for approximating definite integrals, and the Fundamental Theorem of Calculus. Students also learn integration by substitution, finding area under and between curves, displacement and distance from velocity functions, and the average value of a function over an interval.
How StudyPug Helps Utah Calculus Students
- Video lessons broken into short, focused segments for every topic
- Practice problems with step-by-step solutions for every lesson
- Content aligned to Utah Core Standards Math for high school
- Available on any device so students can study at home or on the go
- Free sample lessons available before subscribing
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