f(x)=lim_(x rarr oo){((1+sin pi x)^(t)-1)/((1+sin pi x)^(t)+1)}

lim_(x rarr oo) sin x /x =1

Discus the continuity of the function f(x)=lim_(n rarr oo)((1+sin x)^(n)+In x)/(2+(1+sin x)^(n))

If quad f(x)=lim_(t rarr oo)((| alpha+sin pi x|)^(t)-1)/((| alpha+sin pi x|)^(t)+1),x in(0,6)

if f(x)=lim_(n rarr oo)((1+sin x)^(n)+e^(x))/(1+(1+sin x)^(n)) where x in[-2 pi,2 pi], If p,q denotes number of values of x where f(x) is discontinuous and non-derivable respectively then 'p+q' is equal to

lim_(x rarr oo)x sin(1/x)=

f(x)=lim_(n rarr oo)(tan pi x^(2)+(x+1)^(n)sin x)/(x^(2)+(x+1)^(n)), find lim_(x rarr0)f(x)

If f(x)=lim_(n rarr oo)(tan pi x^(2)+(x+1)^(n)sin x)/(x^(2)+(x+1)^(n)) then

lim_(x rarr oo) (1+f(x))^(1/f(x))

Evaluate lim_ (x rarr 1) (1+sin pi x) ^ (cot pi x.)

lim_ (x rarr oo) x ^ (2) sin ((pi) / (x)) =