To prove: That lim x → c x n = c n for any integer n > 1 , using the fact lim x → c x = c and the result in exercise 2 lim x → c ( f 1 ( x ) ⋅ f 2 ( x ) ⋅ ⋯ ⋅ f n ( x ) ) = L 1 ⋅ L 2 ⋅ ⋯ ⋅ L n .

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Answer 1

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Chapter A.5, Problem 3E

To determine

To prove: That limx→cxn=cn for any integer n>1, using the fact limx→cx=c and the result in exercise 2 limx→c(f1(x)⋅f2(x)⋅⋯⋅fn(x))=L1⋅L2⋅⋯⋅Ln.

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Q2: Find the interval and radius of convergence for the following series: Σ n=1 (-1)η-1 xn n

8. Evaluate arctan x dx a) xartanx 2 2 In(1 + x²) + C b) xartanx + 1½-3ln(1 + x²) + C c) xartanx + In(1 + x²) + C d) (arctanx)² + C 2 9) Evaluate Inx³ dx 3 a) +C b) ln x² + C c)¾½ (lnx)² d) 3x(lnx − 1) + C - x 10) Determine which integral is obtained when the substitution x = So¹² √1 - x²dx sine is made in the integral πT π π a) √ sin cos e de b) √ cos² de c) c Ꮎ Ꮎ cos² 0 de c) cos e de d) for cos² e de πT 11. Evaluate tan³xdx 1 a) b) c) [1 - In 2] 2 2 c) [1 − In2] d)½½[1+ In 2]

Answer 2

Question

Chapter A.5, Problem 3E

To determine

To prove: That limx→cxn=cn for any integer n>1, using the fact limx→cx=c and the result in exercise 2 limx→c(f1(x)⋅f2(x)⋅⋯⋅fn(x))=L1⋅L2⋅⋯⋅Ln.

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Answer 3

Question

Chapter A.5, Problem 3E

To determine

To prove: That limx→cxn=cn for any integer n>1, using the fact limx→cx=c and the result in exercise 2 limx→c(f1(x)⋅f2(x)⋅⋯⋅fn(x))=L1⋅L2⋅⋯⋅Ln.

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Answer 4

Question

Chapter A.5, Problem 3E

To determine

To prove: That limx→cxn=cn for any integer n>1, using the fact limx→cx=c and the result in exercise 2 limx→c(f1(x)⋅f2(x)⋅⋯⋅fn(x))=L1⋅L2⋅⋯⋅Ln.

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Answer 5

Chapter A.5, Problem 3E

To determine

To prove: That limx→cxn=cn for any integer n>1, using the fact limx→cx=c and the result in exercise 2 limx→c(f1(x)⋅f2(x)⋅⋯⋅fn(x))=L1⋅L2⋅⋯⋅Ln.

Answer 6

Chapter A.5, Problem 3E

To determine

To prove: That limx→cxn=cn for any integer n>1, using the fact limx→cx=c and the result in exercise 2 limx→c(f1(x)⋅f2(x)⋅⋯⋅fn(x))=L1⋅L2⋅⋯⋅Ln.

Answer 7

Chapter A.5, Problem 3E

To determine

To prove: That limx→cxn=cn for any integer n>1, using the fact limx→cx=c and the result in exercise 2 limx→c(f1(x)⋅f2(x)⋅⋯⋅fn(x))=L1⋅L2⋅⋯⋅Ln.

Answer 8

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Answer 9

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Answer 10

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Answer 11

Ch. A.5 - Suppose that functions f1(x), f2(x), and f3(x)...Ch. A.5 - Use mathematical induction and the Limit Product...Ch. A.5 - Prob. 3E Ch. A.5 - Prob. 4E Ch. A.5 - Prob. 5E Ch. A.5 - Composites of continuous functions Figure A.27...

To prove: That lim x → c x n = c n for any integer n > 1 , using the fact lim x → c x = c and the result in exercise 2 lim x → c ( f 1 ( x ) ⋅ f 2 ( x ) ⋅ ⋯ ⋅ f n ( x ) ) = L 1 ⋅ L 2 ⋅ ⋯ ⋅ L n .

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To prove: That limx→cxn=cn for any integer n>1, using the fact limx→cx=c and the result in exercise 2 limx→c(f1(x)⋅f2(x)⋅⋯⋅fn(x))=L1⋅L2⋅⋯⋅Ln.

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Chapter A.5 Solutions

To prove: That lim x → c x n = c n for any integer n &gt; 1 , using the fact lim x → c x = c and the result in exercise 2 lim x → c ( f 1 ( x ) ⋅ f 2 ( x ) ⋅ ⋯ ⋅ f n ( x ) ) = L 1 ⋅ L 2 ⋅ ⋯ ⋅ L n .

Concept explainers

Videos

To prove: That limx→cxn=cn for any integer n>1, using the fact limx→cx=c and the result in exercise 2 limx→c(f1(x)⋅f2(x)⋅⋯⋅fn(x))=L1⋅L2⋅⋯⋅Ln.

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Chapter A.5 Solutions

To prove: That lim x → c x n = c n for any integer n > 1 , using the fact lim x → c x = c and the result in exercise 2 lim x → c ( f 1 ( x ) ⋅ f 2 ( x ) ⋅ ⋯ ⋅ f n ( x ) ) = L 1 ⋅ L 2 ⋅ ⋯ ⋅ L n .