Maddox Smith Staff asked 4 years ago

Mathematics for Function

Question 1[12 marks] (a) Determine the following limits(i) lim x!1×3 +3×2 4x +1 3×3 +2×7 ,(ii) lim x!01/(x + 2) + 1/2 x,explaining your reasoning carefully. Do not use l’Hopital’s rule. (b) Find constants a,b 2 R so that the following rules give a function that is continuous on R: (x)=8 > > > < > > > : ax2 1 for x<1 4 for x =1 1 bx for x>1. (c) Let f(x)=3×2 5. Find the derivative of f(x) using the definitionf0(x) = lim h!0f(x + h)f(x) h.