This paper circulates around the core theme of Question 1[12 marks] (a) Determine the following limits together with its essential aspects. It has been reviewed and purchased by the majority of students thus, this paper is rated 4.8 out of 5 points by the students. In addition to this, the price of this paper commences from £ 99. To get this paper written from the scratch, order this assignment now. 100% confidential, 100% plagiarism-free.
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
.
