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(Solved): = 1. The purpose of this question is to show that The notation f(x) ~ g(x) means that limx g ...



=
1. The purpose of this question is to show that
The notation f(x) ~ g(x) means that limx?? g(x)
1
X
? In (1) ² ~ In (x)
1/2

= 1. The purpose of this question is to show that The notation f(x) ~ g(x) means that limx?? g(x) 1 X ? In (1) ² ~ In (x) 1/2 dt in (a) [5 marks] Determine whether the improper integral ? 1 ? In (x) -dx converges. Explain your reasoning. Hint: look at the tangent line of ln(x) at x = 1. (b) [5 marks] Deduce (1). Hint: make sure to verify the assumptions of any theorem you invoke using part (a).


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