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Q1:9.1 Add it up (#integration) For each of the following sums: (i) Estimate the sum for n= 10, 100 and 1000 (you may use computational tools to help, make sure to include supporting code). (ii) Evaluate (or estimate) the limit as n → ∞. (iii) Rewrite the sum as a definite integral and compute it. Compare your results. 2n (a) › Σ ((¹ + :-)²) = (b) Σ (COS ()) 2nSee Answer
Q2:Prove the following equalities and inequalities: $Pdv # 0, $Tds #0 $d(PV) = 0, $d(TS) = 0 $Pdv=-SAT $VdP=-$TdS $VdP = $SATSee Answer
Q3:7. h(x) = = =sin-¹(x) 8. Using derivative rules and the trigonometric identities 1 sin² (8) = (1 - cos(20)), cos² (0) = (1 + cos(20)), show clearly that the function f(x) = sin(x) cos(x) — satisfies properties (a) and (b). 2 (a) f'(x) = cos(2x), (b) ƒ ( 7 ) = 0See Answer
Q4:Q4. Consider an aircraft flying in straight and level flight with total wing area 110 m², wing loading 2600 N/m² and a drag polar of 0.02 +0.06C2, at sea level. The aircraft engines can generate up to 1.8 times the thrust needed to maintain straight and level flight at 175 m/s. Calculate the climb rate that this aircraft could achieve. [10 marks] Q5. Summarise the ways in which the trim of an aircraft can be controlled by a pilot. [6 marks] Q6. Define the aerodynamic centre and why it's a useful point on an aircraft for analysing aerodynamic forces. [4 marks]See Answer
Q5:Use the Comparison Theorem for integrals to determine whether the integrals below are convergent or divergent. Be sure to verify your comparison integral is either less than or greater than the integral you are trying to determine converges or diverges.See Answer
Q6:Suppose ∫ FX DX converges. What does the graph below suggest about the convergence of 9(2) da? Explain your reasoning.See Answer
Q7:Determine if the following statements are true or false. If the statements is true, explain why. • If the statement is false, give an example of a specific function or graph that shows the statement is false AND provide an explanation of how your example shows that the statement is falseSee Answer
Q8:Explain your strategy for evaluating the following indefinite integral. Be sure to explain the reasoning for your strategy and any substitution choices that would be needed to show the following statement is true.See Answer
Q9:Given the rational function 1/(x-1)²(x-2) Show there are no real numbers A and B that make the following partial fraction decomposition true:See Answer
Q10:The goal of this problem is to find a general formula for the area of an ellipse in terms of the lengths of its semi-major and semi-minor axes (denoted by a and b in the figure below).See Answer
Q11:Ed, Jin, and Faye were debating on how to integrate the following the integral:See Answer
Q12:Luca and Maria are debating about how to evaluate the integralSee Answer
Q13:Using full sentences, write a brief summary of the geometric transformation that occurs to the integralSee Answer
Q14:Explain why the areas for each of the following graphs are equal WITHOUT computing their u/du-substitution. It may be helpful to recall that sin(2x) = 2 sin x cosx. areas. Hint: UseSee Answer
Q15:Identify which Jamal's method(s), if any, you would use to integrate the following integrals. Be sure to provide reasoning for your choices.See Answer
Q16:Explain your strategy for evaluating the following indefinite integral. Be sure to explain the reasoning for your strategy and any substitution choices that would be needed to show the following statement is true.See Answer
Q17:Given the rational function 1/(x-1)²(x-2) Show there are no real numbers A and B that make the following partial fraction decomposition true:See Answer
Q18:The goal of this problem is to find a general formula for the area of an ellipse in terms of the lengths of its semi-major and semi-minor axes (denoted by a and b in the figure below).See Answer
Q19:Ed, Jin, and Faye were debating on how to integrate the following the integral:See Answer
Q20:Using full sentences, write a brief summary of the geometric transformation that occurs to the integralSee Answer

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