Question

Find the slope of the function f ( x ) = 3 - 2 x , by the definition of limit.

Answer 1

the slope is -2
`\lim_(n \to \0)( f(x+h)-F(x)) /h \\\\ \lim_(n \to \0) (3-2(x+h)-(3-2x))/h\\ f(x+h)= 3-2(x+h) \\f(x)=3-2x\\ \\\lim_(n \to \0)  (3-2x-2h-3+2x)/h\\\\ \lim_(n \to \0) -2h/h\\  \\ \lim_(n \to \0) -2\\=-2\\\\In all limits, you have to put n goes to 0 (zero)`

Explanation: