When a soft drink is extracted from the inside of a refrigerator, the speed with which its temperature increases after t minutes of being extracted is: (image attached) Estimate the rise in temperature of the soda in the first 6 minutes after it is removed from the refrigerator. Use three intervals of time of the same size Δt.
When a soft drink is extracted from the inside of a refrigerator, the speed with which its temperature increases after t minutes of being extracted is:
(image attached)
Estimate the rise in temperature of the soda in the first 6 minutes after it is removed from the refrigerator. Use three intervals of time of the same size Δt.
In this question, Riemann sum is applied to estimate the rise in temperature of soda.
Riemann Sum
To estimate , Riemann sums are utilised by approximating areas using the areas of rectangles or trapezoids. The width of each rectangle/trapezoid is . Different ways of approximation are available depending on how we
choose the height of the rectangles, including the trapezoidal method.
The Left Hand Rule, the Right Hand Rule, and the Midpoint Rule are three standard methods for the determining height of these rectangles.
- The Left Hand Rule states that the function should be evaluated at the sub-interval's left-hand endpoint and the rectangle should be that height.
- The Right Hand Rule says to evaluate the function at the right endpoint on each sub-interval and make the rectangle that height.
- According to the Mid Point Rule, evaluate the function at the midpoint of each sub-interval and make the rectangle that height.
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