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4. For the series Σ=1+()", does it converge and if so what does it converge to? * n²

4. For the series Σ=1+()", does it converge and if so what does it converge to? * n²

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter6: Applications Of The Derivative
Section6.3: Implicit Differentiation
Problem 42E
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Need help with question 4, 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 ≤ 5 3. Find parametric equations of the tangent line to the curve given by r(t) =< et, t4,t + 3> at the point with t = 0. * ()", does it converge and if so what does it converge to? n² 5. Determine whether the series E-1(−1)" * - is conditionally convergent, n*+n+1 absolutely convergent, or divergent and explain why. 6. Find the radius of convergence and the interval of convergence for Σn-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 of convergence? (x)n n! 100 8. The Maclaurin Series for ex is ex = Σn=0 a. 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 the initial 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) = <t², 0, t³>.
Transcribed Image Text: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 ≤ 5 3. Find parametric equations of the tangent line to the curve given by r(t) =< et, t4,t + 3> at the point with t = 0. * ()", does it converge and if so what does it converge to? n² 5. Determine whether the series E-1(−1)" * - is conditionally convergent, n*+n+1 absolutely convergent, or divergent and explain why. 6. Find the radius of convergence and the interval of convergence for Σn-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 of convergence? (x)n n! 100 8. The Maclaurin Series for ex is ex = Σn=0 a. 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 the initial 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) = <t², 0, t³>.
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