Taylor Polynomials


Introduction

The fundamental idea in differential calculus is that a function can be ``locally'' approximated by its tangent line.

For instance consider the function tex2html_wrap_inline169 near tex2html_wrap_inline171 . Since its derivative at tex2html_wrap_inline173 equals tex2html_wrap_inline175 , the tangent line at tex2html_wrap_inline171 can be written as

displaymath167

In the picture below, the sine function is black, while its tangent line is depicted in red. Close to tex2html_wrap_inline173 , both are quite close!


Try it yourself!

Find an equation for the tangent line of the function tex2html_wrap_inline183 at the point tex2html_wrap_inline185 .

Click here for the answer, or to continue.

Helmut Knaust
Sun Jul 7 22:08:09 MDT 1996

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