First of all, I have a calculus final coming up and I couldn't even do some problems that were apparently basic. I would really appreciate it if someone could break down each question and try to explain to me how they got to the answer. I really don't want to fail this final.
1) The farmer plans to fence a regular pasture adjacent to a river. The pasture must contain 2,000,000 square meters in order to provide enough grass for the herd. What dimensions would require the least amount of fencing if no fencing is needed along the river?
2) A population of 500 bacteria is introduced into a culture and grows in number according to the equation p(t)=500 (1+4t/50+t^2) where t is measured in hours. Find the rate at which the population is growing at t=2.
3) find the horizontal and vertical asymptote of y=2x/x-3
Find the limit.
lim sin x/5x
Prove that the lim f(x) = 2 and lim f(x)=infinity are approaching infinity.
Thank you in advance.