Answer Happy

[20] 2. Series [1] a. A convergent series must have a finite number of terms (summands) True False [4] b. Use the Alternating Series Test to show that the following series converges (-1)¹+6n n² +9 n=1 [5] c. Determine whether the following series converges n=1 4n-3 2n5 [6] d1. Find the first four non-zero terms of the MacLaurin Series Expansion of the following function. How many terms are required to achieve 0.1% accuracy? f(x) = sin²(x) [2] Express the complete expansion as an finite seri s in summation notation. [2]. e. The mechanical stretch response of an artery in expansion is described by a "j-shaped" curve, with a pronounced "toe" region and a stiff final region, as shown in the figure below. The physiological range is indicated in pink. A biomechanical model of the system could be represented with the differential equation: mx + Bx +k(x)x = sin(@at). Without actually attempting to solve the equation, explain how a series expansion of the strain hardening stiffness k(x) could simplify the model so that it could be solved with the tools studied in this course. Pressure 120 mmHg PRESSURE VS DIAMETER physiological range 80 mmHg collagen dominated Diameter elastin dominated collagen elastin