(ii)Show that `underset (x rarr 3) Lt (x/`[x]`)` does not exist.

(a) underset (x rarr 2)lim [x]=……..

Evaluate underset (x rarr 1)Lt (x^4-1)/(x-1)

(a)Evaluate underset (x rarr 0)Lt(sin x^0)/x

Prove that underset (x rarr 0)lim (x^2 sin (1/x))/sin x=0

(i)Evaluate underset (x rarr 3^+)Lt x/[x] and underset(x rarr 3^-) Lt x/[x] .

(a)Let f(x)={(x,if x is an integer),(0,if x is not an integer)) .Show that underset (x rarr 1)Lt f(x)=0 .

Let f(x)={(1,x<1),(ax+b,3

Find underset(x rarr 0)lim (1-cos x)/x .

Evaluate underset (x rarr 0)Lt (sin 3x+7x)/(3x+sin 7x)

Evaluate underset (x rarr 0)Lt [(1-cos 4x)/(x^2)] .