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Calculus I Challenge


Topics (CTs):

Limit and Continuity: Limits and continuity of single variable functions. Computation of limits. Continuity. Limits involving Infinity. L’hospital rule

The derivative:change of rates, rules of derivatives, higher derivatives, chain rule, implicit differentiation, L’Hospital’s rule. Derivative of trigonometric, Logarithmic and Exponential functions.

Applications of derivatives: Maximum and Minimum values increasing and decreasing functions, concavity, sketching of functions, some optimization applications

Integrals:antiderivatives and indefinite integral, fundamental theorem of Calculus, simpler integration techniques.

Methods of integrations: General power formula, basic logarithmic and exponential forms, trigonometric forms, integration by substitution, integration by parts.

Applications of Integrations: In geometry: Finding area under the curve and between two curves, and using integration in physics and other engineering applications.