I need help with the calculus questions. Thank you!

1. "The Prime Directive is not just a set of rules; it's a philosophy" You are a crew member aboard the Starship Interspace. While observing a distant alien planet called Earth, you discovered a function f(r) that is defined and continuous on -co A(h). The CAPE value is an integral taken over the heights h where P(h) > A(h). For this data, the CAPE value is therefore defined as follows: CAPE = 9800 ( P(h) - A(h) ) dh J/ kg. A(h) + 273 The atmosphere is said to have strong instability if 2500 4000. (a) Estimate the CAPE value using left-hand and right-hand Riemann sums with 4 equal subdivisions. Does either of these estimates reach the threshold of strong instability? Do either reach the threshold of extreme instability? (b) Consider the function appearing in the integrand, B(h) = P(h) - A(h) A(h) + 273 You must use derivatives to justify your answer to the following two questions. i. Is B(h) increasing or decreasing on the interval 3 4000. If you cannot rule out the possibility of extreme instability, you will issue a severe thunderstorm watch. Hint: You will need your answer to part (b). i. Using left or right Riemann sums (as appropriate) with 4 equal subdivisions, give an overestimate and an underestimate of the integral P(h) - A(h) 9800 dh. A(h) + 273 ii. Using left or right Riemann sums (as appropriate) with 4 equal subdivisions, give an overestimate and an underestimate of the integral P(h) - A(h) 9800 dh. A(h) + 273 ini. Use your answers to (i) and (ii) to give an overestimate and an underestimate of the CAPE value. iv. Can you be certain whether or not the CAPE value reaches the level of strong instability? v. Should you issue the severe thunderstorm watch