1. ## infinite limits

lim t-->1 t^3/ (t^2-1)^2

I just really want to know if you have to use algebra to factor out the denominator or do i just plug in the values i.e. 0.9 from the left and 1.1 for the right

NEED FOR CLASS AT 10 THIS MORNING!

2. The numerator goes to 1, and the denominator goes to zero. Since the denominator is always positive, the limit is positive infinity. Done.

3. I know the answer i have to do the working using first principle and I want to know how to work it for when the lim t-->1 is coming from the left and for example i use the value 0.9 do i put it in as

(0.9)^3/ ((0.9)^2-1)^2 or (0.9)^3/(0.9-1)(0.9+1)

4. "plugging in values" doesn't evaluate the limit, in some unusual cases, a function can fluctuate quite wildly near the point the limit is evaluated at.

in your case, what you would need to show that no matter how big a number N you choose, you can pick a value of t close enough to 1 so that

t^3/(t^2 -1)^2 > N. the value that will work, will depend on the number N.

5. Thank You so much I wasn't able to see your reply before class but I plugged in the answer and got the value