If`f(x)={x+1/2, x<0 2x+3/4,x >=0` , then `[(lim)_(x->0)f(x)]=` (where [.] denotes the greatest integer function)

Solve x^2-4-[x]=0 (where [] denotes the greatest integer function).

Evaluate int_(0)^(1.5) x[x^2] dx , where [.] denotes the greatest integer function

lim_(xrarr0) [(sin^(-1)x)/(tan^(-1)x)]= (where [.] denotes the greatest integer function)

(lim)_(xvec(-1^)/3)1/x[(-1)/x]= (where [.] denotes the greatest integer function) a. -9 b. -12 c. -6 d. 0

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

Let f(x)=sec^(-1)[1+cos^(2)x], where [.] denotes the greatest integer function. Then the range of f(x) is

If f:R->R is defined by f(x)=[x−3]+|x−4| for x in R , then lim_(x->3) f(x) is equal to (where [.] represents the greatest integer function)

Prove that int_0^x[t]dt=([x]([x]-1))/2+[x](x-[x]), where [.] denotes the greatest integer function.

Draw the graph of f(x) = [x^(2)], x in [0, 2) , where [*] 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 .