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  1. In questions 1.1 to 1.7 below, one or more of the alternatives are correct.  Write the code letter(s) a, b, c, d corresponding to the correct alternative(s) in the answer book.  Marks will be given only if all the correct alternatives have been selected and no incorrect alternative is picked up.

1.6). Which of the following improper integrals is (are) convergent?

  1. $\int ^{1} _{0} \frac{\sin x}{1-\cos x}dx$
  2. $\int ^{\infty} _{0} \frac{\cos x}{1+x} dx$
  3. $\int ^{\infty} _{0} \frac{x}{1+x^2} dx$
  4. $\int ^{1} _{0} \frac{1-\cos x}{\frac{x^5}{2}} dx$
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