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Question 1[12 marks] (a) Determine the following limits

19 / 01 / 2019 Maths

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Question 1[12 marks] (a) Determine the following limits
(i) lim x!1
x3 +3x2 4x +1 3x3 +2x7 ,
(ii) lim x!0
1/(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)=3x2 5. Find the derivative of f(x) using the definition
f0(x) = lim h!0
f(x + h)f(x) h
.


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