Q: Solve for x:
|x² – 2x| = 3
Month: September 2009
Absolute Value
Q: Solve the absolute value problem: |x/2 – 1/3| = 1
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.
Differentiation: Product Rule
Q: Find the derivative of (x² – 5x + 2)*(x – 2/x)
Integration: U-substitution w/ by parts
Q: ∫sin(√x)dx
Polynomial long division example
Q: Use polynomial long division to divide: x²/(1-3x)
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
Integration: multiple “u-substitutions”
Q: ∫x³/√(4 – x2) dx
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
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!]
