Hi, I tried to do the following problems but I didn't get very far.
Find each limit using L'Hopital's rule (if possible; check assumptions before you try to use it!) or otherwise.
lim (tanx/x) as x approaches 0
-->since it's indeterminate form : 0/0, i used the rule and got 0 but the answer is 1.
lim (x^(4x)) as x approaches 0 from the right side
-->i tried to use the rule for it by changing it into a fraction: 1/ x^(-4x) but then when i differentiate it's almost the same thing
a(c) = 5c / e^(2c)
-->how do i find the leading behaviours if there is only one term in the numerator and in the denominator?
thanks!