Question: Use the indicated methods to solve the following problems with nonuniform grids. A curling iron is plugged into an outlet at time t = 0.

Use the indicated methods to solve the following problems with nonuniform grids.

A curling iron is plugged into an outlet at time t = 0. Its temperature T in degrees Fahrenheit, assumed to be a continuous function that is strictly increasing and concave down on 0 ≤ t ≤ 120, is given at various times (in seconds) in the table.

t (seconds) 45 90 110 120 T(t) (°F) 239 311 70 130 200 355 375

a. Approximate 120 T(t) dt 120 in three ways: using a left Riemann sum, a right Riemann sum, and the Trapezoid Rule. Interpret the value of t (seconds) 45 90 110 120 T(t) (F) 239 311 70 130 in the context of this problem.

b. Which of the estimates made in part (a) overestimates the value of 200 355 375 120 T(t) dt 120 Underestimates? Justify your answers with a simple sketch of the sums you computed.

c. Evaluate and interpret in the context of this problem.

t (seconds) 45 90 110 120 T(t) (F) 239 311 70 130 200 355 375 120 T(t) dt 120

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