posted Dec 20, 2018, 4:36 PM by Matthew Grenfell
[
updated May 14, 2019, 4:22 AM
]
 Use
various techniques to evaluate limits, including algebraic manipulation,
graphs, and tables of values
 Use
limit laws to evaluate limits, including sums and products of limits
 Use
the definition of continuity to determine if a function is continuous at a
point or to determine ways to make a function continuous at a point
 Understand
and describe discontinuities on a graph
 Evaluate
limits at infinity and determine equations of horizontal asymptotes
 Understand
the definition of a derivative as a limit of a difference quotient
 Interpret
the derivative at a point on a graph and use the derivative of a function
to determine the equation of a tangent line at a given xvalue
 Determine
the derivative of various functions using the general power rule, product
rule, quotient rule, chain rule, etc.
 Compute
derivatives of exponential, logarithmic, and trigonometric functions
 Compute
derivatives using implicit differentiation and logarithmic differentiation
 Use
the concept of related rates to determine the rate of change of related
variables or quantities
 Determine
the critical numbers (xvalues) of a function
 Use
the Extreme Value Theorem to determine the absolute maximum and minimum
values of a function on an interval
 Use
properties of the first and second derivatives of a function to
algebraically or geometrically determine critical numbers, intervals where
the function is increasing or decreasing, intervals where the function is
concave up or down, the shape of the graph, etc.
 Use
L'Hospital's Rule to evaluate limits and determine when a limit has
indeterminate form
 Use
calculus to solve optimization problems involving an unknown quantity and
a constraint
 Use
Riemann sums to approximate the area under a curve or to approximate the
value of a definite integral
 Evaluate
definite integrals using the Fundamental Theorem of Calculus
 Use
an appropriate substitution to evaluate definite integrals when needed
 Determine
the area between two curves
 Determine
the volume of a solid of revolution using the method of disks/washers
 Evaluating
limits and using the limit laws
 Determine
the derivative of various functions using the general power rule, product
rule, quotient rule, chain rule, etc.
 Compute
derivatives of exponential, logarithmic, and trigonometric functions
 Compute
derivatives using implicit differentiation and logarithmic differentiation
 Derivatives
of inverse trigonometric functions (particularly arctangent, which is most
useful)
 Exponential
growth and decay models (population growth, halflife decay, Newton's law
of cooling)
 Sketching
the graph of a function using information about the function, the first
derivative, and the second derivative
 Evaluate
definite integrals using the Fundamental Theorem of Calculus
 Determine
antiderivatives and indefinite integrals
 Use
an appropriate substitution to evaluate definite integrals when needed

