Test 3 Exam and Solutions - Integration and Approximation Test 3 Closed book and notes No calculators or any other electric device Show your work

# Test 3 Exam and Solutions - Integration and Approximation...

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Integration and Approximation Test 3 Closed book and notes. No calculators or any other electric device. Show your work! problem points score 1 20 2 10 3 15 4 15 5 25 6 15 total 100 Name: Andrew ID: Section: Taylor Series: 1 1 - x = X n =0 x n = 1 + x + x 2 + x 3 + · · · + x n + · · · , R = 1 e x = X n =0 x n n ! = 1 + x 1! + x 2 2! + x 3 3! + · · · + x n n ! + · · · , R = sin x = X n =0 ( - 1) n x 2 n +1 (2 n + 1)! = x - x 3 3! + x 5 5! - x 7 7! + · · · + ( - 1) n x 2 n +1 (2 n + 1)! + · · · , R = cos x = X n =0 ( - 1) n x 2 n (2 n )! = 1 - x 2 2! + x 4 4! - x 6 6! + · · · + ( - 1) n x 2 n (2 n )! + · · · , R = tan - 1 ( x ) = X n =0 ( - 1) n x 2 n +1 2 n + 1 = x - x 3 3 + x 5 5 - x 7 7 + · · · + ( - 1) n x 2 n +1 2 n + 1 + · · · , R = 1 ln(1 + x ) = X n =1 ( - 1) n - 1 x n n = x - x 2 2 + x 3 3 - x 4 4 + · · · , R = 1 (1 + x ) k = X n =0 k n x n = 1 + kx + k ( k - 1) 2! x 2 + k ( k - 1)( k - 2) 3! x 3 + · · · , R = 1 1
2 1. Consider the parametric equationx= lnt, y= 1 +t2.(a) (12 points) Determine the equation of the tangent line to the curve att= 1.