I just had a killer calculus exam and there are two questions I cannot seem to figure out no matter what.
The first one goes:
The limit of (3+1/x)^x as x approaches 0+. Show what the limit is or if it does not exist show why.
I have no clue how to simplify it. I know it exists because it's just asking for the right sided limit, which means it must exist.
As for the integral question it goes like this:
find g'(x) if the g(x)= integral of pi/4 to sin(x^2) of arcsin(t)/(t^2+1) dx
I know that you cannot simply plug in pi/4 and sin(x^2) into the integral.. but I have no idea how to do it otherwise w/o antideriving it, plugging in the pi/4 and sin(x^2) and then deriving it again. But I had no clue how to antiderive arcsin(t).
Anyways, I keep mulling over these questions. If anyone could help me figure them out it would be great!!!
Thank you SO much!