I just need help in answering this question

Nausheen is considering the improper integral where f : [187, co) - R is the function defined by f(z) = 8 arctan(x) + 3x tanh(x) + d 117 ' (24 + 7323 - 74x2 + 93x - 42) 190 for some positive real constant d. To decide whether this integral converges or diverges, Nausheen intends to use the limit form of the comparison test. Help Nausheen complete their argument: First, Nausheen should find some simpler function g : [187, co) -> R such that lim f (z) Click for List x-+00 g(x) To this end, explain to Nausheen why lim arctan(x) + a tanh(x) ) = a -+00 for any constant o. Essay box advice: In your explanation, you don't need to use exact Maple syntax or use the equation editor, as long as your expressions are sufficiently clear for the reader. For example, you can write lim arctan(x) + a tanh(x) ) as 'lim_(x->infinity) [ arctan(x)/x + alpha tanh(x) ]', . [187, co) as '[187, infinity)'. Q S Equation A - A-IX BIUS X X Styles Font Size Words: 0 Then, we can choose, for example, the function defined by the rule g(z) = P where p and q are constants with the values (entering a value for p as a fraction [not a decimal], if necessary, and choose q from the drop-down list.) P= and q= Click for ListOO Since Click for List Click for List Click for List , the improper integral g(x) dx 187 Click for List and so we conclude by the Click for List that the improper integral f(x) da Click for List J187 Having found a method of solving the above problem, Nausheen is now wondering whether any other constant p could have been used in the above procedure. Choose one of the following options: O p can be any positive real number. The choice of p is unique. O p is not unique but p 2 3