Unit 1: Sections 2.1-3.8, JIT: 13
Skill Set

Section 2.1: Rates of Change and Tangents to Curves

Problems Assigned: 1, 3, 9, 10

Assessment Item	Online	Textbook
Find the average rate of change of a function over a given interval. (That is, find the slope of the secant line between two points on a curve.)	1, 3
Find the slope of a curve at a given point using the formula for the slope of a secant line through that point and a nearby point.	10	9
Find an equation of the tangent line to a curve at a given point.	(10)	(9)

Section 2.2: Limit of a Function and Limit Laws

Problems Assigned: 1, 3, 5, 9, 19, 27, 29, 39, 43, 47, 51, 57, 61, 65, 67, 69, 83

Assessment Item	Online	Textbook
Given a graph, find the limit of a function or explain why a limit does not exist.	1
Determine the validity of or interpret a limit statement.		3, 5, 9
Find the limit of a function using the Limit Laws.	19, 27, 29, 39, 57	43, 47, 51, 61, 65
Find the limit of a function using the Sandwich Theorem.		67, 69
Interpret a limit involving a named, but unknown, function. Find the limit of the function.		83

Section 2.3: The Precise Definition of a Limit

Problems Assigned: 7, 11, 15, 17, 23

Assessment Item	Online	Textbook
Given ε and the limit value, use a graph to find a specific δ that satisfies the ε-δ definition of a limit.	7, 11
Given ε and the limit value, algebraically find a specific δ that satisfies the ε-δ definition of a limit.	15, 17, 23

Section 2.4: One-Sided Limits and Limits at Infinity

Problems Assigned: 1, 3, 9, 13, 17, 21, 25, 29, 33, 41, 45, 47, 51, 57, 61

Assessment Item	Online	Textbook
Determine if a given one-sided limit statement is true. If not, explain why.	1
Determine if a given one-sided limit exists. If not, explain why.	9	3
Find a one-sided limit of a function.	(9), 13, 17	(3)
Find a limit involving (sin x)/x.	21, 25, 29, 33
Find a limit at infinity of a function.	41, 45, 47, 51, 57, 61

Section 2.5: Infinite Limits and Vertical Asymptotes

Problems Assigned: 1, 5, 13, 19, 27, 31, 33, 39, 41

Assessment Item	Online	Textbook
Recognize and evaluate an infinite limit.	1, 5, 13, 19
Find all asymptotes (horizontal, vertical, other) of a rational function.	27, 31, 33
Graph a function including all asymptotes.	(27, 31, 33)	39, 41

Section 2.6: Continuity

Problems Assigned: 1, 2, 3, 4, 5, 7, 9, 13, 21, 25, 33, 35, 39, 40, 45, 47, 51, 52

Assessment Item	Online	Textbook
Given a graph, determine it a function is continuous on a given interval. If not, explain why.	1	2, 3, 4
Determine if a function is continuous at a point by definition.	5	7
Find the points (intervals) at which a function is continuous.	13, 21, 25
Determine one-sided continuity.	(1), 33	(2, 3, 4)
Redefine a function with a removable discontinuity so that it is continuous at the given point.	35	9
Determine the value of a constant for which a function is continuous everywhere.		39, 40
Use the Intermediate Value Theorem to show that an equation has at least one solution or a given number of solutions.		45, 47
Find a function which has a given removable or nonremovable discontinuity. Show how the function is discontinuous and explain why it is removable or not.		51, 52

Section 2.7: Tangents and Derivatives at a Point

Problems Assigned: 3, 5, 7, 13, 17, 23, 25, 27, 29, 37, 43

Assessment Item	Online	Textbook
Use a straight edge to make a rough estimate of the slope of a curve at a point.		3
Find the slope of a curve at a given point using the limit definition. (Find an instantaneous rate of change of a function at a given instant.)	5, 7, 13, 17, 27	29
Find the equation for a tangent line to a curve at a given point.	(13, 17)	(25)
Find all points where a function has tangent lines of a given slope.	23	25
Determine if and where a graph has a vertical tangent. Confirm with limit calculations.	37, 43

Section 3.1: The Derivative as a Function

Problems Assigned: 1, 3, 7, 11, 13, 17, 19, 25, 27, 28, 29, 30, 32, 35, 39, 40, 41, 43

Assessment Item	Online	Textbook
Differentiate a function using the definition. (Find the slope of the tangent.)	1, 3, 7, 11, 13, 17, 19, 25	43
Match the graph of a function with the graph of its derivative.	27	28, 29, 30
Given a graph, determine where a function is not differentiable and explain.	32	35
Given a graph, determine where a function is differentiable, continuous but not differentiable, and neither continuous nor differentiable.	39	40, 41
Determine if and where a graph has tangent lines of a given slope. If so, find an equation for a tangent line. If not, explain.		43

Section 3.2: Differentiation Rules for Polynomials, Exponentials, Products, and Quotients

Problems Assigned: 1, 7, 9, 13, 17, 25, 27, 29, 31, 35, 37, 41, 43, 45, 47, 49, 51

Assessment Item	Online	Textbook
Find the derivative of a function using the differentiation rules.	1, 7, 9, 17, 25, 27, 29, 37, 41, 43, 45	13, 31, 35
Find the second derivative of a function.	(1, 7, 9, 37, 41, 43, 45)
Find the derivatives of all orders of a function.	(37)
Given values for functions and their derivatives at a point, find the value of a derivative at that given point.	47
Find the equation for a normal line to a curve.		49a
Find the smallest slope on a curve and where it occurs.		49b
Find equations for the tangents to a curve having specified slope.		49c
Find the tangents to a curve at a given point.	51

Section 3.3: The Derivative as a Rate of Change

Problems Assigned: 1, 5, 7, 9, 13, 15, 17, 21, 25, 28

Assessment Item	Online	Textbook
Find the displacement and average velocity of a body moving on a coordinate line.	1a, 5a
Find the speed and acceleration of a body at a given instant.	1b, 5b	7ab
Determine when, if ever, during a given interval a body changes direction.	1c, 5c	7c
Find the total distance traveled by a body.		(7c)
Solve and interpret a displacement given a function or graph.	9, 13, 15	17
Solve and interpret a rate of change application.	25, 28
Match graphs with a function, its derivative, and its second derivative. Explain reasoning.		21

Section 3.4: Derivatives of Trigonometric Functions

Problems Assigned: 1, 7, 11, 13, 17, 19, 23, 25, 27, 35, 37, 41, 43, 45, 47

Assessment Item	Online	Textbook
Differentiate a function involving trigonometric functions.	1, 7, 11, 13, 17, 19, 23, 25, (45)	27
Graph a trigonometric function with its tangents over a given interval.		(27)
Determine if and where a graph has a tangent line of given slope. If not, explain.	37	35
Find the limit of a trigonometric function.	41	43
Find the velocity, speed, acceleration, and jerk of a body moving on a coordinate line given a trigonometric position function.	45
Determine if a function has a removable discontinuity and, if so, redefine it so that it is continuous at the given point.		47

Section 3.5: The Chain Rule and Parametric Equations

Problems Assigned: 1, 5, 11, 17, 21, 23, 24, 25, 26, 27, 33, 37, 41, 47, 49, 53, 57, 61, 65, 67, 71, 73, 75, 79, 81, 83, 85, 89, 101, 102, 103, 107

Assessment Item	Online	Textbook
Use the Chain Rule to differentiate a composite function.	1, 5, 11, 17, 21, 23, 24, 25, 26, 27, 33, 37, 41, 47, 49, 53, 57, 61, 65, 67, 71
Write a composite function in the form of its two (composing) functions.	(11, 17, 21)
Find the value of a derivative at a given point.	(67, 71), 75, 79a	73
Find the smallest slope of a curve on a given interval. Explain reasoning.	79b
Given parametric equations and a parameter interval for the motion of a particle, identify the particle's path by finding a Cartesian equation.		81, 83, 85, 89
Given parametric equations, find an equation for the line tangent to the curve at a given value of the parameter.	103, 107	101, 102

JIT: 13: Equations of Degree 1 Revisited

Problems Assigned: 1, 2, 3, 4, 5, 6, 7

Assessment Item	Online	Textbook
Solve linear equations involving derivatives		JIT: 1, 2, 3, 4, 5, 6, 7

Section 3.6: Implicit Differentiation

Problems Assigned: 1, 6, 7, 9, 11, 17, 19, 21, 25, 27, 31, 37, 39, 41, 49

Assessment Item	Online	Textbook
Use implicit differentiation to find dy/dx (the first derivative = rate of change)	1, 7, 9, 11, 21	6, 17, 19
Use implicit differentiation to find the second derivative.	(21), 25	(19)
Find the lines that are tangent and normal to a curve at a given point.	31, 37
Use implicit differentiation to find the slope of the tangent line to a curve at a point.	27, 41	39
Find where a curve has parallel tangents.		(39)
Use implicit differentiation to find the slope of the normal line to a curve at a point.		49
Find where a normal line to a curve at a point intersects the curve.		(49)

Section 3.7: Derivatives of Inverse Functions and Logarithms

For additional review, see Just-In-Time Algebra and Trigonometry, Chapter 7.

Problems Assigned: 3, 5, 7, 9, 11, 15, 19, 21, 25, 31, 35, 39, 41, 45, 59, 61, 63, 65, 67, 71, 75, 83, 87, 89, 93

Assessment Item	Online	Textbook
Given an one-to-one function, find its inverse.	3a	5a
Graph a function and its inverse together to verify symmetry about y = x.	3b	5b
Evaluate the derivative of a function at the x-coor of a point and the derivative of its inverse at the y-coor of a point.	3c	5c
Given a differentiable, one-to-one function, a point on the curve and the slope of the curve there, find the derivative of the inverse.	7	9
Find the derivative of a logarithmic (or exponential) function.	11, 15, 19, 25, 31, 35, 39, 59, 63, 65, 67, 75, 83, 87	21, 61, 71
Use logarithmic differentiation to find the derivative.	41, 45, 89, 93

Section 3.8: Inverse Trigonometric Functions

Problems Assigned: 1, 3, 5, 7, 11, 13, 17, 21, 25, 30, 33, 35, 40, 41, 54

Assessment Item	Online	Textbook
Use reference triangles to find the angle given by an inverse trig function.	1, 7, 11	3, 5
Find a limit involving inverse trig functions.	13, 17
Find the derivative of a function involving inverse trig functions.	21, 25, 33, 35, 41	30, 40
Derive a formula for the derivative of an inverse trig function using implicit differentiation.		54