Question

using the limit definition of derivative, find F(x)=x^2+2 at x=2

Answer 1

limit definition= F(x+h)-F(x)\[F(x+h)-F(x)\div h \]

Answer 2

\[ \lim_{h \rightarrow 0} \dfrac {\left( (x+h)^2 + 2 \right) - \left( x^2 + 2 \right)}{h} = \lim_{h \rightarrow 0} \dfrac {x^2 + 2xh + h^2 - x^2}{h} = \] \[\lim_{h \rightarrow 0} \dfrac {2xh + h^2}{h} = \lim_{h \rightarrow 0} (2x + h) = 2x. \]At x = 2, this is 4.