How do you find the limit of #arcsin(x)/ arctan(x)# as x approaches 0?

1 Answer

Answer:

#lim_(x rarr 0) (sin^-1 x)/(tan^-1 x)=1#

Explanation:

We evaluate the limit first

#lim_(x rarr 0) (sin^-1 x)/(tan^-1 x)=0/0#

We apply L'Hospitals Rule

#lim_(x rarr 0) (sin^-1 x)/(tan^-1 x)=lim_(x rarr 0) (d/dx(sin^-1 x))/(d/dx(tan^-1 x))=lim_(x rarr 0) ((1/sqrt(1-x^2)))/((1/(1+x^2)))=1#

God bless....I hope the explanation is useful.