Math Final Study Guide

• Review Math HW

Check units (4.6-5.4)

Summary of Topics by Unit in Study Guide:

Section 4.6: Related Rates and Applications

• Problems involving changes in geometric shapes (e.g., circular infections, water tanks).

• Use of related rates to find how one quantity changes concerning another.

• Key formulas for geometric shapes (e.g., circles, cylinders, hemispheres).

• Practice includes applications of the chain rule and implicit differentiation.

Section 4.7: L’Hôpital’s Rule

• Application of L’Hôpital’s Rule to evaluate limits.

• Conditions and forms where L’Hôpital’s Rule applies (indeterminate forms like 0/0 and ∞/∞).

• Multiple practice problems focused on evaluating limits and verifying applicability.

Section 4.8: Parametric Equations

• Visualization and graphing of parametric curves.

• Finding slopes of parametric curves using derivatives.

• Parameterization of lines and circles.

• Tangent line equations at given parameter values.

Section 5.1 & 5.2: Definite Integrals and Riemann Sums

• Introduction to definite integrals using Riemann sums (left-hand, right-hand sums).

• Approximation of areas under curves.

• Interpretation of integrals as total distance and area.

• Practice estimating integrals using tabular data and graphs.

Section 5.3: Fundamental Theorem of Calculus

• Precise statement and application of the Fundamental Theorem of Calculus.

• Evaluation of definite integrals and their interpretation as area.

• Applications in physical contexts (e.g., water flow and pollution removal).

Section 5.4: Properties of Definite Integrals & Area Between Curves

• Properties of definite integrals (e.g., linearity, additivity).

• Average value of functions over an interval.

• Calculating and interpreting areas between two curves using definite integrals.