Answer:
[tex]e^{3}[/tex]
Step-by-step explanation:
// since evaluating limits of the numerator and denominator would result in an indeterminate form, use the L'Hopital's rule
[tex]\lim_{x \to \ 3} (\frac{\frac{d}{dx} (e^{x} - e^{3} } {\frac{d}{dx} (x-3)} )[/tex]
// calculate the derivative
[tex]\lim_{x \to \ 3} (\frac{e^{x} }{\frac{d}{dx} (x-3)} )[/tex]
[tex]\lim_{x \to \ 3} (\frac{e^{x} }{1} )[/tex]
[tex]\lim_{x \to \ 3} (e^{x})[/tex]
// evaluate the limit
[tex]e^{3}[/tex]
