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a) Find the sum of the following series. 2+(-1)" 3n n=0 b) Σ; n=1 2 n(n+1)(n + 2)*

a) Find the sum of the following series. 2+(-1)" 3n n=0 b) Σ; n=1 2 n(n+1)(n + 2)*

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Q1) Find the sum of the following series. 00 2+(-1)" a) Σ 3n n=0 2 b) Σ n(n + 1)(n+ 2)* n=1 Q2) Determine whether the following series converge absolutely, converge conditionally or diverge. a) Σ n=0 b) Σ n=1 TAT n=1 (-1)^(n!)² (2n)! n² + (-1)" 2n² + 3n (−1)n n³ n¹ +3 Q3) Using power series, 2-1 + cosa IA te [ªr sin(7³)dr within an error less than 10-5. a) evaluate lim I-0 b) estimate Q4) The following parts are independent. 8²z a) Find if z=f(x-y,x+y). əyəx b) Find and classify all critical points of f(x, y) = 2x³ + 6xy² - 3y³ - 150x. Q5) The following parts are independent. a) Find a function f satisfying df (x, y) = (4x³y² + 2x)dx + (2x¹y + 3y²)dy. b) Find the maximum of f(x, y) = x²y² subject to the condition x + y = 10.
Transcribed Image Text:Q1) Find the sum of the following series. 00 2+(-1)" a) Σ 3n n=0 2 b) Σ n(n + 1)(n+ 2)* n=1 Q2) Determine whether the following series converge absolutely, converge conditionally or diverge. a) Σ n=0 b) Σ n=1 TAT n=1 (-1)^(n!)² (2n)! n² + (-1)" 2n² + 3n (−1)n n³ n¹ +3 Q3) Using power series, 2-1 + cosa IA te [ªr sin(7³)dr within an error less than 10-5. a) evaluate lim I-0 b) estimate Q4) The following parts are independent. 8²z a) Find if z=f(x-y,x+y). əyəx b) Find and classify all critical points of f(x, y) = 2x³ + 6xy² - 3y³ - 150x. Q5) The following parts are independent. a) Find a function f satisfying df (x, y) = (4x³y² + 2x)dx + (2x¹y + 3y²)dy. b) Find the maximum of f(x, y) = x²y² subject to the condition x + y = 10.
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