Question

More limit problems; see the attachment for the problem.

Answer 1

infact the question asks for the derivative of the function!!

Answer 2

just put in your function f(x+dx)=2x+2dx-3
f(x)=2x-3
so f(x+dx)-f(x)=2x+2dx-3-2x+3=2dx
so you have 2dx/dx which is equal to 2
so your answer is 2.
Such a limit is a derivative and you will probably have to learn many derivatives later.
The derivative of x^n is n*x^(n-1), but proving that is not as simple as some simpletons might tell you. Most students take these so called formulas for granted, and the teachers who can prove that are rare. The problem is to prove it for real numbers, not just whole numbers(ring Z) - -1,-2,2,3,etc.