Hi, I've got two questions here that I'm stuck on. The first: 2. Relevant equations Find the Limit as x->0 of [(e^4x)-1-4x]/x^2 3. The attempt at a solution So far: I got that the Limit as x->0 is indeterminate form 0/0 so I tried L'Hopital's: to find the Limit as x->0 of [(e^4x)-4]/2x but that gave me a Limit of -3/0 . So I think that means that there's no limit. But the book insists that the Limit is 8. and I have no idea how it got there. the second question I'm confused about is 2. Relevant equations Find the Limit as x->2 of (x+2)/[(x-2)^4] , and explain why L'Hopital's Rule does not apply. 3. The attempt at a solution so The Lim x->2 = 4/0 so it's not 0/0 indeterminate so L'Hopital's isn't applicable. But after that I'm a bit stuck on how to get the Limit. I know that because x can't equal 0 in the denominator that x cannot equal 2. So there's a vertical asymptote there. So...I know I can look at it from each side The Limit as x->0- and as x->0+ . So- The Limit as x->0+=infinity The Limit as x->0-=infinity. is that right? and is their an easier way to find that then just plugging in numbers near x=2? -Thanks, any help would be much appreciated!