**4 Part Calc Experts problem only please … really difficult and challenging, I need help please! details below?**

*The temperature* in the New Year's Day Hinterland is given by T (H) =- A-bcos (piH/12), where T is the temperature in degrees Fahrenheit and H is the number of hours since midnight (0 <T is equal to or less than 24). a) The initial temperature at midnight was -15 degrees Fahrenheit, and at noon on New Year's Day was 5 degrees F. Find A and B b) Determine the average temperature of the first ten hours C) Use the trapezoidal rule with four equal subdivisions to the estimation of the integral of T (H) dH with an upper limit and lower limit d June Find an expression for the rate that the temperature is changing with respect to H.

if T (h) = – A bcos – (piH/12) and T (0) = -15 And t (12) = 5, then -15 =- AB and 5-A = B + (cos (pi) = -1) presents two equations, two unknowns. add: -15 + 5 = (-ab) + (-a + b) -10 =- =- 2a or 2a, as a = 5 and therefore b = 10 b) The average temperature is the integral of the function divided by time elapsed, or 1 / 10 * integral from 0 to 10 (-5-10cos (pih/12)). c) calculate the value of the function at 6, 6.5, 7, 7.5, and 8. You want to add: 0.25 * T (6) + 0.5 * (t (6.5) + t (7) + T (7,5)) + 0.25 * t (8). of half-time is increased by division. Just put half the weitght at each end point. d) t (h) is simply the derivative t (h), which is + bsin (PIH / 2) * pi / 2 (using the chain rule)

**Lose Yourself in Calculus**

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