Course review
Review each learning objective in this topic, then open its concept explanation or question set.
Learning objective
• Understand continuity and differentiability informally. • Use convergence/divergence of limits. • Define derivative from first principles for polynomials; use higher-derivative notation.
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Learning objective
• Evaluate limits of f(x)/g(x) as x approaches a value or infinity. • Use L'Hopital's rule or Maclaurin series for indeterminate forms 0/0 and infinity/infinity. • Repeated use of L'Hopital's rule may be required.
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Learning objective
• Use implicit differentiation and related rates. • Solve optimization problems, including endpoint cases where appropriate.
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Learning objective
• Differentiate tan x, sec x, cosec x, cot x, a^x, log_a x, arcsin x, arccos x and arctan x. • Integrate their derivative forms, including composites with linear functions. • Use partial fractions to rearrange integrands.
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Learning objective
• Use integration by substitution; substitutions are provided where not directly recognizable. • Use integration by parts, including repeated integration by parts.
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Learning objective
• Find area enclosed by a curve and the y-axis over an interval. • Find volumes of revolution about the x-axis or y-axis.
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Learning objective
• Solve first-order differential equations. • Use Euler's numerical method. • Solve separable, homogeneous and first-order linear equations with integrating factor.
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Learning objective
• Use Maclaurin series for e^x, sin x, cos x, ln(1+x) and (1+x)^p. • Obtain other series by substitution, products, integration and differentiation. • Develop Maclaurin series from differential equations.
Start with the concept explanation, then practise to create mastery evidence.