If the function f (x) is defined near x = 0, and f (0) = 0, f ′ (0) = 1, then limx → 0f (x) x = 1

If the function f (x) is defined near x = 0, and f (0) = 0, f ′ (0) = 1, then limx → 0f (x) x = 1

It is easy to know that LIM (X -- > 0) {[f (x) - f (0)] / (x-0)} = f '(0) = 1. = = = > LIM (X -- > 0) [f (x) / x] = 1

If f (x) is defined near x = 0, f (0) = 0, f '(0) = 1, limx approaches 0f (x) / X=
The function f (x) is defined near x = 0, f (0) = 0, f '(0) = 1, then limx tends to 0, f (x) / x =?

Limx tends to 0 f (x) / X
=Limx tends to 0 [f (x) - f (0)] / X
=f'(0)
=1

How to prove that continuous function has: limf (x) = f (limx)

If LIM (x - > x0) f (x) = f (x0), then f is said to be continuous at x0
Is the definition of continuous function