MA103-Mock Midterm and solutions - MA103 Mock Midterm Name...

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MA103 Mock MidtermName:Time Allowed:80 minutesTotal Value:60 marksNumber of Pages:6Instructions:Non-programmable, non-graphing calculators are permitted.No other aids allowed.Check that your test paper has no missing, blank, or illegible pages.Note that test questions appearonbothsides of the paper.Answer in the spaces provided.Show all your work.Insu¢ cient justi°cation will result in a loss of marks.1.[6marks]Write your answer to each of the following questions in the space provided.No justi°cationis necessary.(a)limx!15°1=x=(b)limx!103px°103 =(c) The domain of the functionf(x) = sin°1xis(d) True or False?Ifaandbare any real values, thenln (ab) = lna+ lnb.(e) Iff(x) =jx+ 5j,thenfis not di/erentiable atx=(f) Iff(x) = sin (x),thenf(103)(x) =1
2.[7marks]Consider the functionf(x) =8<:ln (°x)°3x,x± °1°°x2°x°2°°x+ 1,x >°1.(a) Determine iffis continuous atx=°1.(b) Based on our answer to part (a) alone, can we make a conclusion about the di/erentiability offatx=°1?Explain your answer.

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