Answer to Question #75139 in Calculus for Vyea

Question

1) Find the limit or explain why does it not exist

i) lim┬(h→0)⁡〖((x+h)^²-x²)/h〗
ii) lim┬(x→0)⁡〖((x+h)^²-x²)/h〗
iii) lim┬(x→0)⁡〖(1/(2+x)-1/2)/x〗
iv) lim┬(x→0)⁡〖((2+x)^3-8)/x〗

2) Find lim lim┬(∆x→0)⁡〖(f(x+∆x)-f(x))/∆x〗 if

i) f(x) = 4/x
ii) f(x) = x²-4x