Math 180

4. Evaluate(a) lim -3x2x(b) lim 5e-4x(c)lim ln(x+2)

xxx-2+

(d) lim (e -ex)/ (x-1)(e) lim x/ex(f) lim(lnx)/x3

x1xx

5.Graphing Technique: Consider the functionR(x)=x2+ x - 6

x2- x - 12

(i)Find the domain(ii) Find the x-intercept(iii) Find the y-intercept

(iv) Find the HorizontalAsymptote(v) Find the Vertical Asymptote

(vi) AnalyzeR'(x)to find the critical value(s)ofR(x) and the partition number(s) ofR'(x). Draw a sign Chart to determine the interval of decrease and the interval of increaseand any extrema.

(vii)AnalyzeR''(x)to find the partition numbers (if any) for R''(x). Draw a sign chart to determine the interval(s) off up-concavity, and down concavity. Locate any inflection point.

(viii)Sketch the graph ofR(x)