Question

For some unknown function f(x), we are told that lim x --> 0 ( f(x)-3 ) / 5x = 7

Can lim x --> 0 be determined using only this information? if so, find its value.

Answer 1

$\bf \lim\limits_{x\to 0}\ \cfrac{f(x)-3}{5x}=7\\\\ -----------------------------\\\\ \cfrac{f(x)-3}{5x}=7\implies f(x)-3=35x\implies \boxed{f(x)=35x+3}\\\\ -----------------------------\\\\ \lim\limits_{x\to 0}\ \cfrac{\boxed{35x+3}-3}{5x}\implies \cfrac{35x}{5x}\implies 7$