Question

please help, question involving limits!!!!

Answer 1

Given: \[1/\sqrt(x)\] find the equations to the tangent lines at the point (1,1) using \[\lim_{x \rightarrow a} (f(x) - f(a))/(x-a)\]

Answer 2

\[\lim_{x \rightarrow 1}f(x) = \lim_{x \rightarrow 1} ((x ^{-0.5} - 1^{-0.5})/(x - 1))\]\[= \lim_{x \rightarrow 1} (1/\sqrt{x} - 1)/(x-1) = \lim_{x \rightarrow 1} (1/\sqrt{x} - \sqrt{x}/\sqrt{x})/(x-1)\]\[=\lim_{x \rightarrow 1} ((1- \sqrt{x})/\sqrt{x}))/(x-1) = \lim_{x \rightarrow 1} ((1- \sqrt{x})/\sqrt{x}))/ ((\sqrt{x}-1)(\sqrt{x}+1)\]\[= \lim_{x \rightarrow 1} = -1 /(\sqrt{x}(\sqrt{x}+1)) = -0.5\]

Lots of algebraic manipulations ;]