Apply the procedures of differentiation accurately, including implicit and logarithmic differentiation. Apply the differentiation procedures to solve related rates and extreme value problems; obtain point and interval estimates for means and proportions. Draw graphs, using function, its first derivative, and the second derivative. Define the definite integral as a limit of Riemann sums and interpret it as area. Explain the Fundamental Theorem of Calculus, showing how differentiation and integration are related. Evaluate an integral by the method of substitution. Use integrals to calculate areas between curves, volumes, work, and average value of a function. Evaluate integrals, using the techniques of integration by parts, using trigonometric identities and trigonometric substitution, and using partial fractions. Solve separable first-order differential equations. Determine whether or not a sequence of real numbers converges.

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