`lim_(x->k) (x-[x])` , where k is an integer, is equal to (where denotes greatest integer function

int_(-10)^(0)(1(2[x])/(3x-[x])/(2[x])/(3x-[x]))dx is equal to (where [*] denotes greatest integer function.) is equal to (where [*] denotes greatest integer function.)

int_- 10^0 (|(2[x])/(3x-[x]|)/(2[x])/(3x-[x]))dx is equal to (where [*] denotes greatest integer function.) is equal to (where [*] denotes greatest integer function.)

Find the left hand derivative of f(x)= [x] sin (pi x) at x=k. where k is an integer and [.] denotes the greatest integer function.

x→1 lim ​ (1−x+[x−1]+[1−x]) is equal to (where [.] denotes greatest integer function)

lim_(x rarr1)(1+x+[x-1]+[1-x]) is equal to x rarr1 (where [1 denotes greatest integer function)

lim_(x rarr oo) (logx^(n)-[x])/([x]) , where n in N and [.] denotes the greatest integer function, is

Lt_(x to oo) ([x])/(x) (where[.] denotes greatest integer function )=

lim_(xrarr oo) (logx^n-[x])/([x]) where n in N and [.] denotes the greatest integer function, is

lim_(xrarr oo) (logx^n-[x])/([x]) where n in N and [.] denotes the greatest integer function, is

lim_(xto0)[m(sinx)/x] is equal to (where m epsilon I and [.] denotes greatest integer function)