The system of equations x + y + z + u + y + z + 2u v = 1. = 2 z + u + 2v = 3 has (cid:13)a (cid:13)b (cid:13)c (cid:13)d (cid:13)e no solutions a unique solution in(cid:12)nitely many solutions with one parameter in(cid:12)nitely many solutions with two parameters in(cid:12)nitely many solutions with three parameters. Let h(x) = 8< x2 (cid:0) 1 x (cid:0) 1 a (cid:0) 2 for x 6= 1 for x = 1. Then h(x) is continuous everywhere for a equal to (cid:13)a (cid:13)b (cid:13)c (cid:13)d (cid:13)e. 1 x + ln x f 0(x) = 1 x(cid:1) ln(cid:0)px + 1(cid:1) +(cid:16) 1 x. 1 x2 + (cid:0)px + 1(cid:1) x + ln x(cid:1) ln(cid:0)px + 1(cid:1)h (cid:0) (cid:0) e(cid:0) 1 (cid:0)px + 1(cid:1) x + ln x(cid:1) ln(cid:0)px + 1(cid:1)h(cid:0) (cid:0) e(cid:0) 1 (cid:0)px + 1(cid:1) 1 x x(cid:1) ln(cid:0)px + 1(cid:1) +(cid:16) 1.