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Secant line and tangent line formally defined, with calculation example.
Linearizations of functions are defined with an example.
Several important linear approximations.
Linear approximations at x=a of f(x), f(c*x), c*f(x), (f+g)(x), f(x)g(x), f(x)/g(x), and f(g(x)). Includes derivations of each and a worked example.
Problems and answers without full explanation. Finding tangent lines to an ellipse, minimizing surface area of a grain silo, finding the volume of a solid of revolution, computing an antiderivative using trig substitution, and computing an antiderivative using integration by parts.
Definition and equation for the linear approximation of a function at a point. Includes diagrams and examples of basic linearizations.
Relating linear approximation formulas to algebraic concepts of geometric series, the binomial theorem, and the sine function. Includes examples and a diagram for the sine function.
Using linearization to find the mass of a body according to special relativity and the mass of a body as it moves away from the earth.
Definition, including differentials and an applet for graphing a function and its derivative.
Estimating the values of an unknown function using linear approximation.
Method for using iterated linear approximations to find an inverse function.
Three part question involving the tangent lines to the graph of f(x) = 1/x.
Finding the equation for the tangent line to an exponential function through a point not on the graph of the function.
Finding the equation of a tangent line to the graph of a function that is defined with an implicit equation.
Finding a tangent line to the graph of a function through a point not on the graph.
Finding the lines through a given point which are tangent to a hyperbola.
Finding the tangent lines to the graph of the exponential function through a point not on the graph.
Finding the tangent lines to the graph of a function defined with an implicit equation through a point not on the graph.
Two questions, one finding the horizontal tangent lines to a given curve and the other finding where a tangent line to a curve crosses the x-axis.
Using an exponential function to track the movement of a hawk as it chases a mouse.
Finding the tangent line to a curve at a point.
Finding the equation in slope-intercept form of a line tangent to a graph at a given point.
Applet which plots the derivative of a function and shows the relationship between the derivative and the tangent line at a point.
Applet which will show some or all of these problems for a specified function at a chosen point.