`lim_ (x rarr0)` `xlogx `

lim_(xrarr0)(xlogx)

lim_(x rarr0)x(cosec x)

7. lim_(x rarr0)(x(log x)^(2))/(1+x+x^(2))

Evaluate: lim_(x rarr 0) (sin (log (1 + 2x)))/(x)

Let f be a function such that f(xy) = f(x).f(y), AA y in R and R(1 + x) = 1 + x(1 + g(x)) . where lim_(x rarr 0) g(x) = 0 . Find the value of int_(1)^(2) (f(x))/(f'(x)).(1)/(1+x^(2))dx

Let f(x) = x(-1)^([1//x]); x != 0 where [.] denotes greatest integer function, then lim_(x rarr 0) f (x) is :

lim_(x rarr0)sqrt(x)=

lim_(x rarr0)|x|^|cos x|

If lim_(x rarr 0) (cos4x+a cos2x+b)/x^4 is finite then the value of a,b respectively

Let f(x) be a function defined by f(x) = {{:((3x)/(|x|+2x),x ne 0),(0,x = 0):} Show that lim_(x rarr 0) f(x) does not exist.