If `lim _(xto0) (ln cot ((pi)/(4) -beta x))/( tan ax)=1,` then `(alpha)/(beta)=.....`

If lim_(xto0)(log_(e)cot((pi)/4-K_(1)x))/(tanK_(2)x)=1 , then

Find lim_(xto0)(cot^(-1)(1/x))/x

lim_(xto0)(3-3tan((pi)/4-x))/(sin2x) is equal to

If lim_(xto0) (log (3+x)-log (3-x))/(x)=k , the value of k is

Let alpha,betainR be such that lim_(xto0) (x^(2)sin(betax))/(alphax-sinx)=1 . Then 6(alpha+beta) equals___________.

Evaluate lim_(xto0){tan((pi)/4+x)}^(1/x)

If alpha+beta=pi/4 then (1+tan alpha)(1+tan beta)=

lim_(xto0)((1-cosx)(3+cosx))/(x tan 4x) is equal to

Simplify be reducing to a single term : (tan alpha - tan ( alpha - beta))/(1 + tan alpha tan ( alpha - beta))

lim_(xto0) (ln(2+x^(2))-ln(2-x^(2)))/(x^(2)) is equal to