(Solved): 11. A curling iron is plugged into an outlet at time t=0. Its temperature T in degrees Fahrenheit, ...

11. 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 0st? 120, is given at various times (in seconds) in the following table. Answer parts (a) through (c) below. t (seconds) 0 T(t) (°F) 70 (a) Approximate ? 120 120 0 20 130 1 120 Using a right Riemann sum, (Type an integer or decimal 1 T(t) dt in three ways: using a left Riemann sum, a right Riemann sum, and the Trapezoid Rule. Interpret the value of 120 120 45 60 199 239 1 120 1 120 Using a left Riemann sum, 0 (Type an integer or decimal rounded to three decimal places as needed.) 110 TH T(t) dt 90 311 120 ST(1) dt = 0 rounded to three decimal places as needed.) 120 T(t) dt 120 354 374 Using the Trapezoid Rule, 0 (Type an integer or decimal rounded to three decimal places as needed.) 1 In the context of this problem, what does the value of 120 120 0 T(t) dt represent? O A. The maximum temperature of the curling iron on [0,120] OB. The change in temperature of the curling iron over [0,120] OC. The average rate of change of the temperature of the curling iron on [0,120] O D. The average temperature of the curling iron on [0,120] 120 0 T(t) dt in the context of this problem. 1 (b) Which of the estimates in part (a) overestimate the value of 120 Which of the following sketches shows a typical rectangle used when computing the left Riemann sum for this problem? O A. OB. ? O E. Q O F. Q 120 T(t) dt? Which underestimate it? Justify your answers with a simple sketch of the sums you computed. 0 La O F. Q ? Based on the sketch, the left Riemann sum (1) the value of the integral. Which of the following sketches shows a typical rectangle used when computing the right Riemann sum for this problem? O A. Q O B. 10.3 O C. Q O G. O C. n O G. Ay Q Q * G Q ? O D. Ay O H. O D. O H. Q Q Based on the sketch, the right Riemann sum (2) the value of the integral. Which of the following sketches shows a typical trapezoid used when applying the Trapezoid Rule to this problem? O A. Q Based on the sketch, the Trapezoid rule (3) (c) Evaluate and interpret 120 (1) In the context of this problem, what does the value of 120 ST'(1) dt = [ 0 (Type an integer or decimal rounded to three decimal places as needed.) T'(t) dt in the context of this problem. OB. h O equals O has no relationship to O overestimates O underestimates the value of the integral. O A. The change in temperature of the curling iron over [0,120] OB. The average rate of change of the temperature of the curling iron on [0,120] O C. The average temperature of the curling iron on [0,120] O D. The maximum temperature of the curling iron on [0,120] (2) 120 ? T'(t) dt represent? 0 Q Q O underestimates O equals O has no relationship to O overestimates (3) O overestimates O underestimates O equals O has no relationship to O C. k X Q O D. 14