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The expression you’ve provided is:

\[
\lim_{n \to \infty} \sum_{i=1}^{n} \frac{e^{x_i}}{1 + x_i} \Delta x
\]

This is a Riemann sum that approximates an integral as \(n \to \infty\). The sum is defined on the interval \([0, 1]\), which implies that the variable \(x_i\) corresponds to points in this interval, and \(\Delta x\) represents the width of each subinterval in the partition of \([0,1]\).

As \(n \to \infty\), the Riemann sum approaches the integral:

\[
\int_{0}^{1} \frac{e^x}{1 + x} \, dx
\]

Thus, the expression can be interpreted as the limit of the Riemann sum, which converges to the definite integral:

\[
\int_{0}^{1} \frac{e^x}{1 + x} \, dx
\]

Would you like a step-by-step explanation of how to solve this integral?

Here are 5 related questions:
1. How is a Riemann sum used to approximate integrals?
2. What is the interpretation of \(x_i\) and \(\Delta x\) in the Riemann sum?
3. How do you evaluate the integral \(\int \frac{e^x}{1+x} dx\)?
4. What are some techniques to compute complex integrals involving exponential functions?
5. What is the significance of the interval \([0, 1]\) in this specific problem?

**Tip:** Understanding the Riemann sum is a crucial stepping stone to mastering the concept of integrals.

Evaluate the limit and sum provided: lim_{n → ∞} Σ (e^{x_i} / (1 + x_i)) Δx for x_i in [0,1].

Learn how to evaluate the limit and sum lim_{n → ∞} Σ (e^{x_i} / (1 + x_i)) Δx for x_i in [0,1] by converting it into a definite integral. This problem introduces key calculus concepts such as Riemann sums and definite integrals, suitable for undergraduate students studying calculus.

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