enzyme function 34 videos

Limits: A Graphical Approach
Calculus Limits and Continuity
How to determine onesided and twosided limits from the graph of a function.
one sided limits two sided limits limit does not exist piecewise functions left hand limit right hand limit graph graphical approach 
Limits and End Behavior
Calculus Limits and Continuity
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.
limits rational functions limit at infinity limit at negative infinity horizontal asymptotes end behavior 
The Quotient Rule
Calculus Techniques of Differentiation
How to differentiate a quotient of two functions.
differentiation quotient rule product rule derivatives 
Limits: A Numerical Approach
Calculus Limits and Continuity
How to estimate a limit using a table of values.
limits functions table of values numerical approach undefined 
Curve Sketching with Derivatives
Calculus Applications of the Derivative
How to evaluate the limit of a function using continuity.

Optimization Using the Closed Interval Method
Calculus Applications of the Derivative
How to evaluate the limit of a function at points where it is not continuous.

The Definition of the Derivative
Calculus The Derivative
How to define the derivative of a function at a point x=a.
average rate of change slope secant line instantaneous rate of change tangent line limits derivative difference quotient 
Concavity and Inflection Points
Calculus Applications of the Derivative
How to show that a function is discontinuous at a point x=a because it is not defined there.

Economics: Marginal Cost & Revenue
Calculus Applications of the Derivative
How to interpret the derivatives of the cost and revenue functions as marginal cost and marginal revenue.
cost revenue profit marginal cost marginal revenue derivatives of cost and revenue 
An Important Limit
Calculus The Derivative
How to interpret the value of a limit important in the derivative of exponential functions.
limits natural logarithm numerical approximation 
Optimization Using the First Derivative Test
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.

The First Derivative Test for Relative Maximum and Minimum
Calculus Applications of the Derivative
How to use an algebraic approach to find onesided limits of a rational function, and how these limits can be used to find a vertical asymptote.

OneSided Limits
Calculus Limits and Continuity
How to use onesided limits to show that a limit does not exist.
one sided limits two sided limits limit does not exist piecewise functions left hand limit right hand limit table of values numerical approach 
Infinite Limits; Vertical Asymptotes
Calculus Limits and Continuity
How to use onesided limits to find a vertical asymptote.
one sided limits infinity limit does not exist rational functions left hand limit right hand limit table of values numerical approach vertical asymptote