`lim x→(2^+) { x } sin( x−2 ) /( x−2)^2 =` (where [.] denotes the fractional part function) a. 0 b. 2 c. 1 d. does not exist

undersetlim_(Xrarr2^(+)) {x}(sin(x-2))/((x-2)^(2))= (where {.} denotes the fractional part function)

If f(x)={x^2}-({x})^2, where (x) denotes the fractional part of x, then

Solve : x^(2) = {x} , where {x} represents the fractional part function.

if f(x) ={x^(2)} , where {x} denotes the fractional part of x , then

f(x)=sqrt((x-1)/(x-2{x})) , where {*} denotes the fractional part.

(lim)_(X-> (-7)([x]^2+15[x]+56)/("sin"(x+7)"sin"(x+8))= (where [.] denotes the greatest integer function) a. is 0 b. is 1 c. is -1 d. does not exist

lim_(x->0) {(1+x)^(2/x)} (where {.} denotes the fractional part of x (a) e^2−7 (b) e^2−8 (c) e^2−6 (d) none of these

If [dot] denotes the greatest integer function, then (lim)_(xvec0)x/a[b/x] a. b/a b. 0 c. a/b d. does not exist

Evaluate int_(0)^(2){x} d x , where {x} denotes the fractional part of x.

If f(x) = (x^n-a^n)/(x-a) , then f'(a) is a. 1 b. 1/2 c. 0 d. does not exist