5 limx→3ex-e3x-3Apply L'Hospital Rule=limx→3ex-e3x-3=limx→3ddxex-e3ddxx-3=limx→3ex1 ddxe3=0 , ddxx=1 , ddx3=0, ddxex=ex=e3Ans e3

Solve 5 question

5 . \lim_{x \to 3} \frac{e^{x} - e^{3}}{x - 3} A p p l y L' H o s p i t a l R u l e = \lim_{x \to 3} (\frac{e^{x} - e^{3}}{x - 3}) = \lim_{x \to 3} \frac{\frac{d}{d x} (e^{x} - e^{3})}{\frac{d}{d x} (x - 3)} = \lim_{x \to 3} \frac{e^{x}}{1} [\frac{d}{d x} e^{3} = 0, \frac{d}{d x} x = 1, \frac{d}{d x} 3 = 0, \frac{d}{d x} e^{x} = e^{x}] = e^{3} (A n s . e^{3})