prove-lim-x-0-e-x-1-x-1-

Question Number 157104 by zakirullah last updated on 19/Oct/21

p r o v e \lim_{△ x \to 0} \frac{e^{△ x} - 1}{△ x} = 1

Answered by puissant last updated on 19/Oct/21

\lim_{Δ x \to 0} \frac{e^{Δ x} - 1}{Δ x} \sim \lim_{Δ x \to 0} \frac{1 + Δ x - 1}{Δ x} = 1

Commented by zakirullah last updated on 20/Oct/21

t h a n k s a l o t

Answered by Fresnel last updated on 20/Oct/21

li \underset{Δ x ⇢ 0}{m} \frac{e^{Δ x} - 1}{Δ x} = l i \underset{Δ x ⇢ 0}{m} \frac{e^{Δ x} - e^{0}}{Δ x - 0} = e^{0} = 1 {b e c a u s e f}^{'} (x) = e^{x} f o r f (x) = e^{x} a n d l i \underset{x ⇢ 0}{m} \frac{f (x) - f (0)}{x - 0} = f^{'} (0) .

Commented by zakirullah last updated on 20/Oct/21

g r e a t s i r!