MATH1A: CALC/ANAL GEOM I
Limits and continuity, analyzing the behavior and graphs of functions, derivatives, implicit differentiation, higher order derivatives, related rates and optimization word problems, Newton's Method, Fundamental Theorem of Calculus, and definite and indefinite integrals. (C-ID: MATH 210) PREREQUISITE: Mathematics 8B with a grade of 'C' or better.
- Explain and evaluate limits in general, at infinity, and at particular points. Do it algebraically, graphically and numerically, utilizing technology.
- Use continuity to describe the behavior of a function and its differentiability.
- Explain the concept of a derivative graphically, numerically, algebraically, and verbally.
- Demonstrate the ability to differentiate polynomials, exponential, logarithmic, rational, implicit, and trigonometric functions. Be able to compute higher order derivatives of these functions.
- Model and solve related rates and optimization problems.
- Analyze and graph functions w/o a calculator. Use derivatives to identify max and min, pts. of inflection, and concavity.
- Calculate limits using L'Hopital's Rule. Be able to determine whether it's applicable or not.
- Use technology to estimate roots using Newton's Method.
- Explain and apply the Fundamental Theorem of Calculus. Use it to evaluate definite and indefinite integrals. Compute basic antiderivatives.
- Use technology to evaluate the definite integral using the Right Hand, Left Hand, and Midpoint Rules. Do Riemann sums.