`underset(x to a)lim {:(tanx-tan a)/(sin a-sin x):}=`

underset(x to 0)"Lt" (tan 6x.tan 5x)/(sin 3x sin 4x)=

underset(x to 0)"Lt" (x tan 7x)/(sin 3x sin 4x)=

Find the limits : (a) underset(x to oo)lim ((2x^(2)+3)/(2x^(2)+5))^(8x^(2)+3) (b) underset(x to 0)lim ((1+tan x)/(1+tan x))^(1//sin x) (c ) underset(x to 1)lim (1+sin pi x)^(cot pi x) (d) underset(x to a)lim ((sin x)/(sin a))^(1//(x-a)) (a ne kpi," with k integer")

Value of underset(x to 0)lim (a^(sin x)-1)/(sin x) is

Evaluate : underset (x rarr 0)lim (3x-tan 4x)/(x+sin x) .

underset(x to 0)"Lt" (e^(tan x)-1)/(sin x)=

Evaluate the following limits : Lim _( xto 0) (tan x - tan a)/(sin a - sin x )

underset(x to 0)"Lt" (sin x)^(tan x)=

underset(x to oo)lim {sin sqrt(x+1)-sin sqrtx)=

underset(xrarr0)lim (sin4x)/(sin2x) is: