| 1. Find the limit of a function |
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| 2. Find one-sided and infinite limits |
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| 3. Identify when a function is continuous or not continuous |
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| 4. Understand and use the limit definition of the derivative |
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| 5. Determine if a function is differentiable |
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| 6. Compute basic derivatives |
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| 7. Apply the product rule and quotient rule for derivatives |
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| 8. Find the derivative of expressions involving trigonometric functions |
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| 9. Apply the chain rule for differentiation |
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| 10. Compute the derivative of an inverse function |
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| 11. Use implicit differentiation to find tangents to arbitrary curves |
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| 12. Find the derivative of expressions involving exponential and logarithmic functions |
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| 13. Set up and solve a related rate question. |
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| 14. Use linear approximation to find the approximate value of a function |
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| 15. Find critical points of a function, determine minima and maxima |
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| 16. State and understand graphically Rolle's theorem and the mean value theorem |
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| 17. Use the first derivative to identify increasing/decreasing, and use the first derivative test |
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| 18. Determine the concavity of a function, and locate inflection points |
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| 19. Use the second derivative test to identify local minima and maxima |
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| 20. Compute limits of a function at infinity, and identify horizontal asymptotes |
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| 21. Set up and solve an optimization problem |
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| 22. Identify an indeterminate limit, and use L'Hopital's rule to evaluate it |
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| 23. Understand Newton's method algorithmically and graphically |
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| 24. Compute antiderivatives of elementary functions |
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| 25. Estimate the area under a curve using a finite sum |
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| 26. Express the area under a curve as a definite integral and a Riemann sum |
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| 27. Understand and apply the fundamental theorem of calculus (part 1) |
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| 28. Evaluate definite integrals using the fundamental theorem of calculus (part 2) |
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| 29. Simplify integrals of even and odd functions |
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| 30. Use the substitution technique |
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