there is a careless mistake somewhere whcih i cant spot in my equation
find the limit of ( 9x +1 ) ^( cot x) as x tends to 0 from the positive direction.
to solve this question, i let y = ( 9x +1 ) ^( cot x)
hence ln y = (cot x) ln (9x+1)
as x tends to 0 from the positive direction, y tends to 1.
lim exp ( ln y) = exp ( lim (ln y)) = exp (0) = 1
but if i were to check back my answers, i did not get an answer of 1.
here is my working:
lim exp ( ln y) = exp ( lim (ln y)) = exp ( lim ( cot x ln ( 9x +1))) = exp (lim ( ln ( 9x +1 ) / tan x )) = exp ( 9 cos ^2 x / ( 9x+1)) by l hopital rule.
which will give me exp (9) instead of my answer of exp (o).