2 4 marks for each of the following indicate whether

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2.[4marks]For each of the following, indicate whether the given statement is true (T) or false (F) bywritingTorFin the space provided.(a) Since the functionf(x) =1xis decreasing on the intervals(°1;0)and(0;1), it is impossibleto °ndx1andx2in the domain offsuch thatx1< x2andf(x1)< f(x2).Answer:(b) Iff00(x0) = 0, thenfhas a point of in±ection atx0.Answer:(c) The graph of a function can have, at most, two horizontal asymptotes.
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3.[7marks]Evaluate each of the following limits.(a)limx!
(b)limx!0+x°sinx4.[8marks]Find an equation of the tangent to the curve given below, at the point°0;12±:6 sin°1(x+y) =°²x2°exy³
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5.[10marks]Consider the functiony=f(x) =10 lnxx2.(a) Determine if the graph offhas any vertical asymptotes and any horizontal asymptotes, justifyingyour answers by calculating relevant limits.

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