• #### Approximating Area Using Rectangles - Problem 1

##### Math›Calculus›The Definite Integral
How to estimate the area between a curve and the x-axis with left- and right-hand sums.
• #### Approximating Area Using Rectangles - Problem 3

##### Math›Calculus›The Definite Integral
How to estimate the area between a curve and the x-axis with left- and right-hand sums.
• #### Approximating Area Using Rectangles - Problem 2

##### Math›Calculus›The Definite Integral
How to estimate the area under a curve, f = x^2 +1, with left- and right-hand sums.
• #### Average Value of a Function - Problem 2

##### Math›Calculus›The Definite Integral
How to use definite integrals to find the average value of a function, f= 12x/(x^2 + 16), over an interval [a,b].
• #### Computing Definite Integrals using Substitution - Problem 3

##### Math›Calculus›The Definite Integral
How to evaluate definite integrals using the method of substitution.
• #### Computing Definite Integrals using Substitution - Problem 2

##### Math›Calculus›The Definite Integral
How to evaluate definite integrals of rational functions by using the method of substitution.
• #### Instantaneous Velocity - Problem 1

##### Math›Calculus›The Derivative
How to estimate the instantaneous velocity of an object from a graph of position vs. time by computing slopes of secant lines over shorter and shorter intervals of time.
• #### Instantaneous Rate of Change - Problem 1

##### Math›Calculus›The Derivative
How to estimate the instantaneous rate of change of the amount of a drug in a patient's bloodstream by computing average rates of change over shorter and shorter intervals of time, and how to represent this rate of change on a graph.
• #### Intervals of Increase and Decrease - Problem 3

##### Math›Calculus›Applications of the Derivative
How to show that the limit does not exist by showing that the left-hand limit does not equal the right-hand limit.
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• #### Intervals of Increase and Decrease - Problem 1

##### Math›Calculus›Applications of the Derivative
How to use one-sided limits to show that a limit does not exist.
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• #### Critical Points - Problem 3

##### Math›Calculus›Applications of the Derivative
How to determine one-sided and two-sided limits from the graph of a function.
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• #### Critical Points - Problem 1

##### Math›Calculus›Applications of the Derivative
How to determine one-sided and two-sided limits from the graph of a function.
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• #### Curve Sketching with Derivatives - Problem 2

##### Math›Calculus›Applications of the Derivative
How to evaluate the limit of a function using continuity.
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• #### Concavity and Inflection Points - Problem 2

##### Math›Calculus›Applications of the Derivative
How to show that a function is discontinuous at a point x=a because its limit and its value at x=a are different.
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• #### Optimization Using the Closed Interval Method - Problem 1

##### Math›Calculus›Applications of the Derivative
How to evaluate the limit of a function at points where it is not continuous.
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• #### Curve Sketching with Derivatives - Problem 4

##### Math›Calculus›Applications of the Derivative
How to evaluate the limit of a function at points where it is not continuous.
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• #### Optimization Using the Closed Interval Method - Problem 3

##### Math›Calculus›Applications of the Derivative
How to evaluate the limit of a function as x goes to infinity (or minus infinity), and how to determine the horizontal asymptote of its graph.
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