Evaluate: `("lim")_(xvec0)(tanx)/x` where `[dot]` represents the greatest integer function

Evaluate : [lim_(x to 0) (tan x)/(x)] , where [*] represents the greatest integer function.

Evaluate ("lim")_(xvec(5pi)/4) [sinx+cosx], where [.] denotes the greatest integer function.

Prove that [lim_(xto0) (tan^(-1)x)/(x)]=0, where [.] represents the greatest integer function.

Given ("lim")_(xvec0)(f(x))/(x^2)=2,w h e r e[dot] denotes the greatest integer function, then (a) ("lim")_(xvec0)[f(x)]=0 (b) ("lim")_(xvec0)[f(x)]=1 (c) ("lim")_(xvec0)[(f(x))/x] does not exist (d) ("lim")_(xvec0)[(f(x))/x] exists

Prove that [lim_(xto0) (sinx)/(x)]=0, where [.] represents the greatest integer function.

Evaluate: int_0^(100)x-[x]dx where [dot] represents the greatest integer function).

Evaluate: ("lim")_(xvec0)(1-cos2x)/(x^2)

("lim")_(xvec0)[(sin(sgn(x)))/((sgn(x)))], where [dot] denotes the greatest integer function, is equal to (a)0 (b) 1 (c) -1 (d) does not exist

Evaluate: int_0^((5pi)/(12))[tanx]dx , where [dot] denotes the greatest integer function.

Let f(x)={cos[x],xgeq0|x|+a ,x<0 The find the value of a , so that ("lim")_(xvec0) f(x) exists, where [x] denotes the greatest integer function less than or equal to x .