Prove that:`lim_(x to0)log(1+sinx)/(x)=1`

Prove that lim_(xto0)((sinx)/(x))=1 (x being in radians ) and hence Show that lim(x to 0) ((tan x)/(x)) = 1 .

lim_(x rarr0)(log(1+x))/(x)=1

Prove that lim_(x to 0) sinx/(log_e (1+x)^(1/2)) = 2

prove that lim_(xrarr0) log_(e)((sinx)/(x))=0

Prove that: lim_(x rarr 0) (log(1+x)+sinx)/(e^(x)-1)=2

Lt_(x to0)(sinx^(2))/(|x|)=

Prove that: lim_(x to 0)(sqrt(1+x)-1)/(log(1+x))=(1)/(2)

Prove that lim_(x rarr 0) (log(1+x^3))/(sin^3 x)=1 .

Show that : lim_(xto0)(sinlog(1+x))/(log(1+sinx))=1

Evaluate the following limits: Show that lim_(x to0) ((tanx)/(x))^(1//x^(2))=e^(1//3)