Re: DSE 2006 paper discussion

Posted by Gayyam on Jun 19, 2014; 6:57pm
URL: http://discussion-forum.276.s1.nabble.com/DSE-2006-paper-discussion-tp7591391p7593135.html

For 16, the question states that the matrix is singular. Thus, det(A) = 0.

Had it been non-zero, the sign would've changed. But here, it stays the same.

For 37, f(x) = (x^2 + 2*x - 1)/x = x + 2 - 1/x.

Now, as x tends to 0, you can see that -1/x will heavily outweigh x+2, therefore f(x) tends -1/x at values of x close to 0. Therefore the y axis is an asymptote.
As x tends to infinity, x+2 heavily outweighs -1/x. Therefore, f(x) tends x+2 for large x. Thus, y=x+2 is also an asymptote.