Question 9 10 p Consider the geometric series (-1)-**. Let S = T. (-1)-**** (1) Give...
Let Consider the geometric series M-1 (-1)^-1 got7 Sm = Enci (1) Give S2 (-1)n-1 21+1 gon (2) What area and r of the this geometric series? (3) Determine algebraically (without using a calculator) if the series is convergent or divergent and why. (4) Find the sum algebraically if it is convergent.
31 Consider the geometric series 2001 (-1)-1 Let Sm = 2-1 (-1)^-1 2071 (1) Give S2 (2) What are a and r of the this geometric series? (3) Determine algebraically (without using a calculator) if the series is convergent or divergent and why. (4) Find the sum algebraically if it is convergent.
Question 10 Co Consider the telescoping series LGT) (1) Let the mth partial sum Sm = (-) Give (1) S = (ii) S2 = (11) S = (iv) In terms of m, Sm (2) Compute lim, (3) Determine if the series + S 00 (-) is convergent or divergent. Give the exact sum if it is convergent. TO Lop 12pt Paragraph BIU A 2 TY BEY B
Question 3 8 pts Evaluate algebraically (without using a calculator) the improper Integral e de if it is convergent. Show why if it is divergent. Show your work in detail 12pt Paragraph B Ι Ο Α e T! EP TO
Consider the telescoping series Σ. (Η -- (1) Let the mth partial sum Sm = m- vnts). 1 va). Give (1) S = (ii) S2 = (iii) S3 (iv) In terms of m. Sm (2) Compute limmo Sin (3) Determine if the series. The most ama vonta) is convergent or divergent. Give the exact sum if it is convergent.
р Question 5 Consider the region that is bounded by y = and y= Væ. Show your work in detail. (1) Sketch the region and find algebraically the intersections of y = ? and y = V. Label your scales. (2) Find exactly the following without using a calculator (i) total mass: m (ii) the first moment about the x-axis: M, (iii) the y coordinate of the centroid (x.y) of the region R. 12pt Paragraph Β Ι Ο Α Αν...
Question 11 Use the Limit Comparison Test to determine if the series ... first. -10 ++1 is convergent or divergent. Give your choices of , and compute the limit C =lim,- 12pt Paragraph BIVA 2 T? EI TO D р Owords </
i 10 (1 point) Consider the series -. Let s, be the n-th partial sum; that is, in +9 10 Sn = i +9 Find 84 and so S4 S8 =
14 1. (10 marks) Let C be the curve 27x - y = 0 between y=0 and y=4. Sketch the graph of this curve. In each part, set up, but do not ovaluate, an integral or a sum of integrals that solves the problem. (a) Find the area of the surface generated by revolving C about the x-axis by integrating with respect to x (6) Find the area of the surface generated by revolving C about the y-axis by integrating...
Question 1 Consider the derivation of the Black-Scholes model of option pricing. Let S=S(t) be the underlying stock price at time t and let f=f(S, t) be the option price at time t. a) Write down the value P of the portfolio defined in the Black-Scholes model. [2 marks] b) Use Itô’s lemma to find an expression for the change Δf in the discrete time Δt. [5 marks] c) Use the expression you have found in point b) to find...