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10 Cards in this Set
- Front
- Back
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Removable Discontinuities |
Occur when the function has a limit (holes in the graph). |
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Non-removable Discontinuities |
Occur when the limit of the function does not exist (jumps and vertical asymptotes). |
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Non-differentiability |
1. Holes 2. Jumps 3. Vertical Asymptotes 4. Sharp Turns 5. Vertical Tangents |
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Average Rate of Change |
The slope between two points. |
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Instantaneous Rate of Change |
The slope at a single point. It is usually found by using a derivative. |
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Speed |
The absolute value of velocity. |
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Displacement |
The net change in position (final position - original position). |
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Implicit Differentiation |
Differentiate both sides with respect to x, remember the y' "hook on factor" and remember to use the Product Rule for xy terms. |
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Critical Numbers |
X-values where f' is zero or undefined (cannot be domain restrictions) |
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Procedure for u-substitution |
1. Let u = radicand 2. Solve for x 3. Differentiate the equation from Step 2 4. Find dx 5. Substitute u-expressions for x-expressions in the integral 6. Integrate 7. Substitute back, so that your final answers is again in terms of x |
