Question

lim e^x−e^3​/ x−3
x→3​

Answer 1

$\lim \limits_{x \to3} { \frac{ {e}^{x} - {e}^{3}}{x - 3} }$

$\sf \purple{put \: \blue{x - 3 = y}}$

$\implies\lim \limits_{y \to0} { \frac{ {e}^{y + 3} - {e}^{3}}{y} }$

$\implies {e}^{3} \lim \limits_{y \to0} { \frac{ {e}^{y } - 1}{y} }$

$\sf \purple{ we \: know \: that : }$

$\blue{ \boxed{\lim \limits_{a \to0} { \frac{ {e}^{a } - 1}{a} } = 1}}$

$\implies {e}^{3}.1$

$\orange{ \therefore {e}^{3} }$

HOPE IT HELPS!!