Express the limit as an integral. S 4 lim (7(x)² - 2(x ) ³)Ax over [0, 4] n→ ∞ i = 1 2 3 7x²-x³ x) dx X

Calculus: Early Transcendentals
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ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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**Express the Limit as an Integral**

Given the following limit expression:

\[
\lim_{{n \to \infty}} \sum_{{i=1}}^{n} \left( 7(x_i^*)^2 - 2(x_i^*)^3 \right) \Delta x \text{ over } [0, 4]
\]

we are asked to express this limit as an integral.

**Correct Integral Form:**

The correct form of the integral is:

\[
\int_{0}^{4} \left( 7x^2 - 2x^3 \right) \, dx
\]

**Error Identification:**

- The image includes a box with \((7x^2 - x^3)\) next to a red 'x', indicating an error.
- The function inside the integral must be \(7x^2 - 2x^3\) instead of \(7x^2 - x^3\).

The integral correctly representing this limit should thus be:

\[
\int_{0}^{4} \left( 7x^2 - 2x^3 \right) \, dx
\]
Transcribed Image Text:**Express the Limit as an Integral** Given the following limit expression: \[ \lim_{{n \to \infty}} \sum_{{i=1}}^{n} \left( 7(x_i^*)^2 - 2(x_i^*)^3 \right) \Delta x \text{ over } [0, 4] \] we are asked to express this limit as an integral. **Correct Integral Form:** The correct form of the integral is: \[ \int_{0}^{4} \left( 7x^2 - 2x^3 \right) \, dx \] **Error Identification:** - The image includes a box with \((7x^2 - x^3)\) next to a red 'x', indicating an error. - The function inside the integral must be \(7x^2 - 2x^3\) instead of \(7x^2 - x^3\). The integral correctly representing this limit should thus be: \[ \int_{0}^{4} \left( 7x^2 - 2x^3 \right) \, dx \]
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