AP Calculus AB Pacing and Alignment Guide

Chapter 2 Solutions Manual  (Access Restricted)

2.1 Learning Targets

I can write the equation of a tangent line to a curve at a point by approximating the slope of the tangent line using slopes of secant lines.

I can describe the concepts of average versus instantaneous velocity, described numerically, graphically, and in physical terms.

2.2 Learning Targets

I can use a table of values to estimate the value of a limit.

I can use a graphing device to estimate the value of a limit.

2.3 Learning Targets

I can evaluate a limit and justify each step by indicating the appropriate Limit Law(s).

I can prove a limit by using the Squeeze Theorem.

2.5 Learning Targets

I can use the definition of continuity and the properties of limits to show that the function is continuous at the given number a.

I can use the definition of continuity and the properties of limits to show that the function is continuous on a given interval.

I can use the Intermediate Value Theorem to show that there is a root to an equation in a specified interval.

2.6 Learning Targets

I can compute an infinite limit.

I can describe the geometric and limit definitions of horizontal asymptotes, particularly as they pertain to rational functions.

2.7 Learning Targets

I can use the instantaneous velocity to solve real-world problems.

I can apply instantaneous rates of change to other real-world applications. (i.e. population growth, cell phone use)

I can find the instantaneous velocity of a real-world problem given a position function.

I can write the equation of the tangent line to a curve at a given point. (Using definition 1 and equation 2)

I can describe how a function can fail to be differentiable.

I can find higher derivatives (2nd and higher) and interpret the meanings in real-world applications.

I can find the derivative of a function using the definition of a derivative using derivative notation.

I can sketch the derivative function given a graph of the original function.