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A Function f(x)\mathrm { f } ( \mathrm { x } )

question 42

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A function f(x) \mathrm { f } ( \mathrm { x } ) , a point c\mathrm { c } , the limit of f(x) \mathrm { f } ( \mathrm { x } ) as xx approaches c\mathrm { c } , and a positive number ε\varepsilon is given. Find a number δ>0\delta > 0 such that for all x,0<xc<δf(x) L<εx , 0 < | \mathrm { x } - \mathrm { c } | < \delta \Rightarrow | \mathrm { f } ( \mathrm { x } ) - \mathrm { L } | < \varepsilon .
- f(x) =4x+9,L=3,c=3f ( x ) = - 4 x + 9 , L = - 3 , c = 3 , and ε=0.01\varepsilon = 0.01

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