Understand the integral definition of the natural logarithm function and its use in defining both the natural exponential function and the meaning of irrational exponents.
Use calculus to produce accurate graphs of functions containing exponential and/or logarithmic expressions
Define and use the hyperbolic and inverse hyperbolic functions.
Differentiate, and integrate transcendental functions, including exponential, logarithmic, hyperbolic, and inverse trigonometric functions, and evaluate limits of functions that contain these transcendentals
Evaluate indeterminate forms, using L’Hôpital’s Rule and logarithmic differentiation when appropriate.
Integrate a wide variety of functions by using appropriate techniques including parts, partial fraction decomposition, trigonometric substitution, and numerical methods such as Simpson’s Rule
Evaluate improper integrals.
Use appropriate tests to determine whether an infinite series converges or diverges and to determine whether or not an alternating series converges absolutely.
Produce a Maclaurin or Taylor series, as appropriate, to represent a function and determine the interval of convergence of the series.
Perform operations, including differentiation and integration, on power series.
Graph conic sections, including those with translated and/or rotated axes.
Graph parametric and polar curves and find areas of polar regions.
Calculate the arc length of parametric and polar curves and find the equations of tangents to such curves.
Perform limits, derivatives and integrals of transcendental functions including logarithmic, exponential, hyperbolic and inverse trigonometric functions.
Integrate functions using appropriate methods including integration by parts, decomposition, trigonometric substitution and Simpson’s rule.
Perform Calculus of polar curves and parametric curves including slope, arc length and area.
Determine whether infinite series converge or diverge using appropriate tests.
Calculate a Taylor series and its interval of convergence, and perform operations on power series for use in computations.