How do you evaluate the limit #tanx/(4x)# as x approaches #0#?

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Answer 1 · 2016-08-28T10:06:52

#1/4#

#lim_(x to 0) (tan x)/(4x)#

#= 1/4 lim_(x to 0) (sin x)/x 1/(cos x)#

as we know that

#lim_(x to 0) (sin x)/x =1#

and

#lim_(x to 0) 1/(cos x) =1#

then the limit of product/quotient is product of limits

#=1/4 lim_(x to 0) (sin x)/x lim_(x to 0) 1/(cos x)#

#implies 1/4 * 1 * 1 = 1/4#