On problem set 3, problem 2A-12 (d), we are supposed to find the quadratic approximation of ln(cos(x)). In the solution, the first step says that it approximates ln(1 - x^2/2). Why is it okay to take that step? I understand that the quadratic approximation of cos(x) ~~ 1 - x^2/2. Is it a general rule that Q(ln(x)) ~~ ln(Q(x))? (Where Q(x) means the quadratic approx of x).

[Also I thought there was some kind of tool to let you enter equations that looked like equations?]

jd

Question

On problem set 3, problem 2A-12 (d), we are supposed to find the quadratic approximation of ln(cos(x)). In the solution, the first step says that it approximates ln(1 - x^2/2). Why is it okay to take that step? I understand that the quadratic approximation of cos(x) ~~ 1 - x^2/2. Is it a general rule that Q(ln(x)) ~~ ln(Q(x))? (Where Q(x) means the quadratic approx of x).

[Also I thought there was some kind of tool to let you enter equations that looked like equations?]

jd