To evaluate the limit

$\lim_{{x \to 1}} (x + 1)e^x$

we proceed by direct substitution, as the function $(x + 1)e^x$ is continuous at $x = 1$.

1. Substitute $x = 1$ into $(x + 1)e^x$: $(1 + 1)e^1 = 2e$

Thus, the answer is:

$\lim_{{x \to 1}} (x + 1)e^x = 2e$

Would you like further details or have any questions?

Here are some related questions you might find helpful:

1. How would you evaluate $\lim_{{x \to 0}} x \cdot e^x$?
2. What steps are used to evaluate limits involving exponential functions?
3. How does the continuity of exponential functions affect limit evaluation?
4. What is the general behavior of $e^x$ as $x$ approaches different values?
5. How would you solve $\lim_{{x \to \infty}} \frac{x}{e^x}$?

Tip: When solving limits with exponential functions, direct substitution is often effective if the function is continuous at the point of interest.