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realiza la grafica y marca la curva y los rectangulos de aproximacion y define si es subestimacion o si es sobreestimacion

The graph above shows the function \( f(x) \) along with the rectangles used for the left and right endpoint approximations.

- **Green rectangles** represent the left endpoint approximation.
- **Orange rectangles** represent the right endpoint approximation.

### Analysis:
- **Right Endpoint Approximation:** The area under the orange rectangles is slightly larger than the actual area under the curve, indicating an **overestimation** (sobreestimación).
- **Left Endpoint Approximation:** The area under the green rectangles is slightly smaller than the actual area under the curve, indicating an **underestimation** (subestimación).

These observations align with typical behavior, where right endpoints usually overestimate when the function is increasing, and left endpoints underestimate.

Would you like further details or have any questions?

Here are 5 related questions to expand your understanding:
1. How does the accuracy of the approximation change with different values of \(\Delta x\)?
2. What happens if we use midpoint approximation instead of left or right endpoints?
3. How can you calculate the exact area under the curve using integration?
4. How does the nature of the function (increasing or decreasing) affect the estimation?
5. Can this method be used for functions that are not continuous or have discontinuities?

**Tip:** For a more accurate approximation, consider using the trapezoidal rule or Simpson's rule, especially for functions that change rapidly.

Explore how to approximate the area under a curve using left and right endpoint methods in calculus. Learn about overestimation and underestimation and their implications. Suitable for advanced high school students and calculus enthusiasts.

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