x in two places 14 videos
-
Substitutions Involving e^x or ln(x)
Calculus Antiderivatives and Differential Equations
How to use the method of substitution when the antiderivatives involve e^x or ln[x].
substitution antidifferentiation exponential functions logarithmic functions power functions -
Continuity
Calculus Limits and Continuity
How to determine whether a function f(x) is continuous at a particular point x=a.
limits definition of a function continuous at a point domain of a function -
Limits: A Graphical Approach
Calculus Limits and Continuity
How to determine one-sided and two-sided 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 -
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 -
The Derivative Function
Calculus The Derivative
How to define the derivative function f'(x).
derivative limits the derivative function -
The Product Rule
Calculus Techniques of Differentiation
How to differentiate a product of two functions.
differentiation derivative formula power functions the product rule of derivatives -
The Quotient Rule
Calculus Techniques of Differentiation
How to differentiate a quotient of two functions.
differentiation quotient rule product rule derivatives -
Continuous Functions
Calculus Limits and Continuity
How to determine whether a function f(x) is continuous everywhere on its domain.
limits definition of continuous function domain of a function power functions exponential functions logarithmic functions -
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.
-
Derivatives of Polynomial Functions
Calculus The Derivative
How to compute the derivative of a polynomial function using two properties of the derivative.
the constant multiple rule the sum rule of derivatives polynomial functions derivative -
Critical Points
Calculus Applications of the Derivative
How to find a two-sided limit by investigating one-sided limits.
-
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 -
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.
-
One-Sided Limits
Calculus Limits and Continuity
How to use one-sided 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
