Q:  Solve for x:

|x² – 2x| = 3

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# Absolute Value

Q:  Solve the absolute value problem:  |x/2 – 1/3| = 1

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# Slope of the Tangent Line

Q:  Find the point(s) on the graph of the function f(x) = (x² + 6)(x – 5) where the slope of the tangent line is -2.

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# Differentiation: Product Rule

Q:  Find the derivative of (x² – 5x + 2)*(x – 2/x)

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Q:  ∫sin(√x)dx

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# Polynomial long division example

Q:  Use polynomial long division to divide:  x²/(1-3x)

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# Increasing/Decreasing & Relative Extrema

Q:  Find:

(a) the intervals where f(x) is increasing, the intervals where f(x) is decreasing, and

(b) the relative extrema of f(x) = -2x³ -9x² + 60x -8

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# Integration: multiple “u-substitutions”

Q:  ∫x³/√(4 – x2) dx

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# Average Rate of Change

Q:  Find the average rate of change of y if x changes from 2 to 5 in the function y = x² + 2x

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# More integration by parts

Q:  ∫ x arctanx dx

A:  Integration by parts again:  ∫udv = uv – ∫vdu

[Review some older examples of “integration by parts” if you are new to this!]

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