Need help with question 1, thank you. 1. Find the area bounded by r = cos 0 for -π/2 ≤0 ≤π/2.2. Find the length of the r(t)= , 1 ≤ t ≤ 53. Find parametric equations of the tangent line to the curve given byr(t) = at the point with t = 0.*()", does it converge and if so what does it converge to?n²5. Determine whether the series E-1(−1)" * - is conditionally convergent,n*+n+1absolutely convergent, or divergent and explain why.6. Find the radius of convergence and the interval of convergence forΣn-on (x-2).4. For the series Σn=n=1;7. Find the Taylor Series for cos x centered at π/2. What is the radius ofconvergence?(x)nn!1008. The Maclaurin Series for ex is ex = Σn=0a. Find T3(x), the 4th degree Taylor Polynomial approximation of ex.b. Use T3(x) to find an approximate value for e¹/².c. Find an upper bound for the error in this approximation.9. Find parametric equations for the line through (1, -2, 2) and perpendicular to and .10. Find an equation for the plane through (1, 3, 1), (2, 1, 1) and (-1, 4, 2).11. Find the position r(t) of an object if the acceleration is a(t) = and theinitial position is r(0) = and the initial velocity is v(0) = ..12. Find the curvature as a function of t of the curve r(t) = .

Question

Need help with question 1, thank you. 1. Find the area bounded by r = cos 0 for -π/2 ≤0 ≤π/2.2. Find the length of the r(t)= <9t, 4t³/2, t²>, 1 ≤ t ≤ 53. Find parametric equations of the tangent line to the curve given byr(t) =< et, t4,t + 3> at the point with t = 0.*()", does it converge and if so what does it converge to?n²5. Determine whether the series E-1(−1)" * - is conditionally convergent,n*+n+1absolutely convergent, or divergent and explain why.6. Find the radius of convergence and the interval of convergence forΣn-on (x-2).4. For the series Σn=n=1;7. Find the Taylor Series for cos x centered at π/2. What is the radius ofconvergence?(x)nn!1008. The Maclaurin Series for ex is ex = Σn=0a. Find T3(x), the 4th degree Taylor Polynomial approximation of ex.b. Use T3(x) to find an approximate value for e¹/².c. Find an upper bound for the error in this approximation.9. Find parametric equations for the line through (1, -2, 2) and perpendicular to<1, 0, 1> and <1, 1, 0>.10. Find an equation for the plane through (1, 3, 1), (2, 1, 1) and (-1, 4, 2).11. Find the position r(t) of an object if the acceleration is a(t) = <6t, 4, -32> and theinitial position is r(0) = <0, 0, 1> and the initial velocity is v(0) = <50, 0, 128>..12. Find the curvature as a function of t of the curve r(t) = .

Accepted Answer

Given r=cosθ for -π2≤θ≤π2