tg

tg
tgt

Tuesday, 26 March 2013

LOCAL BEHAVIOR of FUNCTIONS PART 1


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 . 
Post a Comment