a) considering the identity...
(1)
... and the fact that is...
(2)
... so that is...
(3)
... we conclude that is...
(4)
b) considering that for is...
(5)
... we conclude that is...
(6)
Kind regards
I've already solved this porblem using L'Hospital rule, and now I'm required to solve it without using this rule, rather using the given condition.
Find:
Lim (sinx)^tanx
x-->pi/2
Given that: Lim (1+1/x)^x= e
x-->infinity
The answer is, as you might have guessed, 1. But, can anyone do it absolutely without using L'Hopital rule? I tried to do, but it was only elegant solution, so that's worthless.
a) considering the identity...
(1)
... and the fact that is...
(2)
... so that is...
(3)
... we conclude that is...
(4)
b) considering that for is...
(5)
... we conclude that is...
(6)
Kind regards
Hey, your no. (2) is completely wrong. You get it in the form (0/0) not negative infinity. So the solution is just elegant. I just need to find the limit given that condition (meaning using that condition, instead of L'Hospital rule). So... if anyone can please help me.
Problem: Compute without use of L'hopital's rule
Solution (1): Let so . Finally we can see that . Now in the neighborhood of zero so that and lastly noting that we may conclude that . And once again appealing to asymptotic equivalence so .
Solution (2): Let so that . Letting turns this limit into . But (why?). So that