Suppose that the two functions f(x) and g(x) both tend to infinity then surely f(x) + g(x) also tends to infinity? How can you prove this though? Similarly f(x)*g(x) would also tend to infinity wouldn't it? f(x) - g(x) and f(x)/g(x) wouldn't tend to anything though surely since infinity minus infinity and infinity over infinity are both undefined. Can anyone help me?