Need Explanation for finding limits

”
Can someone explain & teach me how to find the limit, I’m having trouble solving this kind of questions now and my test is coming up in 3 days:
As x approaches negative infinity. x^4+5x^2+1
As x approaches positive infinity. (x^2-3x+7)/(x^3+10x-4)
As x approaches positive infinity. (x^2-3x+7)/(x^3+10x-4)
As x approches 0: (cos(2x) – 1)/(cos(x)-1)
As x approches 3: (x^4-81)/(2x^2-5x-3), I don’t understand this one at all since both top and bottom parts become 0?

Thanks for the help!!