MATH161

Use graphical and numerical evidence to estimate limits, and to identify situations where limits fail to exist.

Apply rules of limits to calculate limits.

Use the limit concept to determine where a function is continuous.

Use the Intermediate Value Theorem to identify an interval where a continuous function has a root.

Use the limit definition to calculate a derivative, or to determine when a derivative fails to exist.

Calculate derivatives (of first and higher orders) with pencil and paper, without table or calculator or computer algebra software, using: linearity of the derivative; rules for products and quotients and the chain rule; rules for constants, powers, and trigonometric and exponential functions; and rules for inverse functions, including logarithms and inverse trigonometric functions.

Use the derivative to find tangent lines to curves.

Calculate derivatives of functions defined implicitly.

Interpret the derivative as a rate of change.

Solve problems involving rates of change of variables subject to a functional relationship.

Calculate the linearization of a differentiable function at a point.

Use differentials (linearization) to approximate the change in value of a function due to a small change in its argument.

Find critical points, and use them to locate maxima and minima.

Use critical points and signs of first and second derivatives to sketch graphs of functions.

Use the first derivative to find intervals where a function is increasing or decreasing.

Use the second derivative to determine concavity and find inflection points.

Apply the first and second derivative tests to classify critical points.

Use Differential Calculus to solve optimization problems.

Find antiderivatives of functions.

Use antiderivatives to solve first-order differential equations of the form dy/dx = f(x) and separable first-order differential equations.

Use sigma notation to represent, manipulate and evaluate finite sums.

Use the definition to calculate a definite integral as a limit of approximating sums.

Apply the Fundamental Theorem of Calculus to evaluate definite integrals and to differentiate functions defined as integrals.

Calculate elementary integrals with pencil and paper, without calculator or computer algebra software, using: linearity of the integral; rules for powers (including exponent +1) and exponentials, the six trigonometric functions and the inverse sine, tangent and secant; and simple substitution.

Use integration to find the area under curves and the area between curves.

Use the relation between the derivative of a one to one function and the derivative of its inverse.

Relate logarithms and exponentials to any base to the natural logarithm and exponential.

Calculate derivatives of logarithmic, exponential and inverse trigonometric functions.

Use logarithmic differentiation.

Use models describing exponential growth and decay.

Apply L'Hpital's Rule to evaluate limits of indeterminate forms.

Apply L'Hpital's Rule to determine relative rates of growth of functions.