Determine whether the series is convergent or divergent. 1 + 37 n =1 convergent O divergent If it is convergent, find its sum. (If the quantity diverges, enter DIVERGES.) XConsider the following differential equation. 2y" + y'-y =0 Exercise (a) For what values of r does the function y = ex satisfy the equation? Part 1 of 3 To determine the values of r for which efx satisfies the differential equation, we substitute f(x) = ex in the equation, 2f " ( x ) + f ' ( x) - f (x) = 0. Thus, we need to find f '(x) and f "(x). f(x) = erx F' ( x ) = re ( rx) X f " ( x ) = 12*e(rx) X Submit Skip (you cannot come back) Exercise (b) If ri and r2 are the values of r that you found in part (a), show that every member of the family of functions y = aefix + be/2* is also a solution. Part 1 of 3 We must decide whether of "(x) + f '(x) - f(x) = 0 for f(x) = ae*/2 + be-x. We have f '(x) = and f "(x) = Submit Skip (you cannot come back)Find the exact length of the curve. 12 = 4(x + 1)5, ox0 14.32 XFind the exact length of the curve. x=e+et, y = 5 - 2t, Ost$5 Step 1 For a curve given by parametric equations x = ((t) and y = g(t), arc length is given by 2 2 dx L = + dy dt dt dt. We have x = e + e , y = 5 - 2t, 0 s t $ 5. dx 50, = and dy dt dt