Limits Graphs Analytically and Asymptote

Which of the following actions are appropriate for finding a limit at infinity? Look for multiple answers.

Find the limit. Hint: Where is the horizontal asymptote?

Find the limit. Hint: Where is the horizontal asymptote?

$$\lim_{x\rightarrow\infty}\ \frac{2x-3}{4x\ +1}$$  

$$\lim_{x\rightarrow\infty}\left(\frac{5}{x^2+1}\right)$$  = 
Hint:  Where is the horizontal asymptote?

$$\lim_{x\rightarrow\infty}\left(\frac{4x}{x+3}\right)$$  = 

$$\lim_{x\rightarrow\infty}\left(2x^3+3x-1\right)=$$  
Hint:  Think of the end behavior of an odd and positive polynomial.

$$\lim_{x\rightarrow-\infty}\left(x^2+3x-1\right)=$$  
Hint:  Think of the end behavior of an even and positive polynomial.

$$\lim_{x\rightarrow\infty}e^x=$$  
Hint:  Think of the end behavior of an exponential function.

Which statement is true about slant asymptotes?