Calculus II

Evaluating limits analytically

• Evaluate a limit using properties of limits

• Develop and use a strategy for finding limits

• Evaluate a limit using dividing out and rationalizing techniques

• Evaluate a limit using the Squeeze Theorem

Continuity and one-sided limits

•  Determine continuity at a point and continuity on an open interval

• Determine one-sided limits and continuity on a closed interval

• Use properties of continuity

• Understand and use the Intermediate Value Theorem

Infinite limits

•  Determine infinite limits from the left and from the right

• Find and sketch the vertical asymptotes of the graph of a function

Implicit differentiation

•  Distinguish between functions written in implicit form and explicit form

• Use implicit differentiation to find the derivative of a function

Related Rates

•  Find a related rate

• Use related rates to solve real-life problems

A summary of curve sketching

•  Analyze and sketch the graph of a function

Optimization

•  Solve applied minimum and maximum problems

Newton’s method

•  Approximate a zero of a function using Newton’s Method

Differentials

•  Understand the concept of a tangent line approximation

• Compare the value of the differential, with the actual change in y, delta y 

• Estimate a propagated error using a differential

• Find the differential of a function using differentiation formulas

Antiderivatives and indefinite integration

• Write the general solution of a differential equation

• Use indefinite integral notation for antiderivatives

• Use basic integration rules to find antiderivatives

• Find a particular solution of a differential equation

Area

• Use sigma notation to write and evaluate a sum

• Understand the concept of area

• Approximate the area of a plane region

• Find the area of a plane region using limits

Riemman Sums and definite integrals

• Understand the definition of a Riemann Sum

• Evaluate a definite integral using limits

• Evaluate a definite integral using properties of definite integrals

The fundamental theorem of calculus

•  Evaluate a definite integral using the Fundamental Theorem of Calculus

• Understand and use the Mean Value Theorem for Integrals

• Find the average value of a function over a closed interval

• Understand and use the Second Fundamental Theorem of Calculus

• Understand and use the Net Change Theorem

Integration by substitution

• Use pattern recognition to find an indefinite integral

• Use a change of variables to find an indefinite integral

• Use the General Power Rule for Integration to find an indefinite integral

• Use a change of variables to evaluate a definite integral

• Evaluate a definite integral involving an even or odd function

Numerical integration

•  Approximate a definite integral using the Trapezoidal Rule

• Approximate a definite integral using Simpson’s Rule

• Analyze the approximate errors in the Trapezoidal Rule and Simpson’s Rule