-
Evaluate limits of functions
Assessment Strategies
Oral, Written, Graphic and/or Skill Assessment
Criteria
use L'hopital's rule to determine the limit
use the correct limit notation
determine where functions are continuous or discontinuous
evaluate limits of various functions at specific points
evaluate one-sided limits of various functions at specific points
evaluate infinite limits
-
Calculate derivatives of algebraic functions
Assessment Strategies
Oral, Written, Graphic and/or Skill Assessment
Criteria
use the formal definition of the derivative to find the derivative of an algebraic function
use appropriate derivative notation
evaluate derivatives at specific values within the domain of differentiable functions
differentiate algebraic functions using the product rule
differentiate algebraic functions using the quotient rule
differentiate algebraic functions using the chain rule
differentiate algebraic functions using generalized power rules
differentiate algebraic functions implicitly
calculate higher order derivatives of algebraic functions
use the Mean Value Theorem for derivatives
-
Calculate derivatives of trigonometric functions
Assessment Strategies
Oral, Written, Graphic and/or Skill Assessment
Criteria
use appropriate derivative notation
evaluate derivatives at specific values within the domain of inverse trigonometric functions
evaluate derivatives at specific values within the domain of trigonometric functions
differentiate trigonometric functions using the product rule
differentiate trigonometric functions using the quotient rule
differentiate trigonometric functions using the chain rule
differentiate trigonometric functions using generalized power rules
differentiate trigonometric functions implicitly
calculate higher order derivatives of trigonometric functions
-
Calculate derivatives of exponential functions
Assessment Strategies
Oral, Written, Graphic and/or Skill Assessment
Criteria
use appropriate derivative notation
evaluate derivatives at specific values within the domain of exponential functions
differentiate exponential functions using the product rule
differentiate exponential functions using the quotient rule
differentiate exponential functions using the chain rule
differentiate exponential functions implicitly
calculate higher order derivatives of exponential functions
differentiate exponential functions with different bases
-
Calculate derivatives of logarithmic functions
Assessment Strategies
Oral, Written, Graphic and/or Skill Assessment
Criteria
use appropriate derivative notation
evaluate derivatives at specific values within the domain of logarithmic functions
differentiate logarithmic functions using the product rule
differentiate logarithmic functions using the quotient rule
differentiate logarithmic functions using the chain rule
differentiate logarithmic functions using generalized power rules
differentiate logarithmic functions implicitly
calculate higher order derivatives of logarithmic functions
differentiate a function using logarithmic differentiation
differentiate logarithmic functions with different bases
-
Use derivatives to solve applied problems
Assessment Strategies
Oral, Written, Graphic and/or Skill Assessment
Criteria
solve related rate applications
solve optimization applications
determine equation of a tangent line through a given point on a curve
determine equation of a normal line through a given point on a curve
use derivatives to establish relationships between position, velocity, and acceleration
approximate the change in a function using linearization or differentials
-
Analyze the graph of a function using derivatives
Assessment Strategies
Oral, Written, Graphic and/or Skill Assessment
Criteria
use the first derivative to find critical points of a function
determine absolute extreme values of a function
determine relative extreme values of a function
use the first derivative to find intervals on which a function is increasing or decreasing
use the second derivative to find intervals on which a function is concave up or concave down
find the inflection points of a function
sketch a curve using calculus techniques
-
Calculate indefinite integrals of functions
Assessment Strategies
Oral, Written, Graphic and/or Skill Assessment
Criteria
use appropriate integral notation
calculate antiderivatives of algebraic functions
find the constant of integration given an initial condition
calculate antiderivatives of trigonometric functions
calculate antiderivatives of exponential functions
calculate antiderivatives that result in inverse trigonometric functions
calculate antiderivatives that result in logarithmic functions
-
Calculate definite integrals of functions
Assessment Strategies
Oral, Written, Graphic and/or Skill Assessment
Criteria
use the fundamental theorem of calculus to evaluate an integral
use a definite integral to calculate the area under a curve
use an integral to determine a total area
use appropriate integral notation
-
Calculate area using calculus techniques
Assessment Strategies
Oral, Written, Graphic and/or Skill Assessment
Criteria
calculate the surface area of a solid of revolution using integrals
find the area of a region between curves using integrals
find the area between two curves by integrating horizontally and vertically
-
Use integrals to solve applied problems
Assessment Strategies
Oral, Written, Graphic and/or Skill Assessment
Criteria
use an integral to calculate an average value
calculate volume of a solid of revolution using the disk/washer method
calculate volume of a solid of revolution using the shell method
use integrals to calculate arc length
-
Use substitution to calculate integrals
Assessment Strategies
Oral, Written, Graphic and/or Skill Assessment
Criteria
calculate indefinite integrals using substitution
calculate definite integrals using substitution
change the limits of integration within a substitution problem
calculate integrals of transcendental functions using substitution
calculate integrals of algebraic functions using substitution