S1. Consider the function f(x)=|2x-3|+3.(a) What are the domain and range of the function?(b) Sketch its graph.(c) Show that fis continuous atx=32.S2. Where does the normal line to the parabola y=x-x2at the point (1,0) intersect the parabolaa second time?[8 marks]S3. Use L'Hopital's Rule to evaluatelimx1+cosxsinxS4. Determine the solution set of the inequality |x2+x|>1.S5. Consider a function h(x) differentiable at all points on its domain. h(x)is increasing atx=aifh'(a)>0; likewise his decreasing atx=aifh'(a)<0. Show that(a)f(x)=1+x1-x,x1,is always increasing;(b)g(x)=1-x1+x,x-1,is always decreasing.S6. Evaluate(a)limx(x-3)(2x+5)x2-8x-3(b)limx0x2+42-25x2S7.In each of the following, find the general term of the sequence and determine whether thesequence converges; ifit does, find its limit.[6 marks](a){-12,15,-110,117,-126,dots}(b){,-1,,-1,,-1,dots}S8. Consider the function[6 marks]f(x)=x-72x2-13x-7