We start with straightforward problems on tangent/normal lines and Taylor polynomial. Then we pass to approximation of functions values with control of error and various applications of Taylor polynomial. At the end we include some non-trivial problems on tangent line.
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For each the following functions, find the equations of the tangent line and the normal line to its graph at the indicated point.
For each the following functions, find the Taylor polynomial with indicated center and degree.
Use Taylor's polynomial of specified degree to approximate the given quantity. Then estimate the error of this approximation using Lagrange's form of the remainder.
Use tangent line to approximate given functions for small values of x. Then estimate the error of this approximation using Lagrange's form of the remainder.
Use Taylor's polynomial of specified degree to approximate the given quantity. Then estimate the error of this approximation using Lagrange's form of the remainder.
In the following problems find tangent line(s) to a given function that satisfy a given condition.