求壹道英文微積分題！

1.The horizonal asymptote:First when x goes to positive infinite，we can use L 'Hospital displine,then the function becomes 2*x(x→+∞)=+∞.Similarily when x→-∞,the function becomes -∞.From these, there exists none horizonal asymptote.

2.The vertical asymptote:From the function we know that the meaningless point is x=4.When x→4-, the function=[(x-4)^2+8(x-4)+7-16+32]/(x-4)=limx→4-(x-4)+8+limx→4-23/(x-4)=0+8+0=8.Similarily,When x→4+,the function is 8.Then, the vertical asymptote is f(x)=8.

3.The oblique asymptote:Assume the oblique asymptote is f(x)=kx(x→∞ ).When x→∞ k=f(x)/x=(x^2+7)x(x-4)=1( L 'Hospital displine).Then the oblique asymptotes are f(x)=±x.

Over.