It seems you've uploaded an image, but the resolution is low. I’ll analyze what I can see:

The image appears to relate to Riemann sums, used for approximating the area under a curve, often linked to integral calculus.

• The title mentions "left, middle, right" which are typically methods for choosing points within intervals to approximate the area under a curve.

• There are three graphs below the text, each likely showing different types of Riemann sum approximations:

  1. Left Riemann Sum (first graph): Uses the left endpoint of each interval to approximate.
  2. Midpoint Riemann Sum (middle graph): Uses the middle point of each interval.
  3. Right Riemann Sum (third graph): Uses the right endpoint of each interval.

The purple regions represent the areas being summed, and they change based on the approximation method.

Would you like me to explain how each of these methods works in detail or clarify anything specific from this image?

Here are some follow-up questions for better understanding:

1. How are left, midpoint, and right Riemann sums calculated?
2. What happens to the approximation when the number of subintervals increases?
3. How do Riemann sums relate to definite integrals?
4. Can you describe the advantages or disadvantages of each method (left, right, midpoint)?
5. How would you use Riemann sums to approximate the area of a real-world function?

Tip: Increasing the number of intervals in a Riemann sum usually improves the accuracy of the approximation!