if `f(x)=|[xcosx,2xsinx,xtanx],[1,x,1],[1,2x,1]| ` find `lim_(x->0) f(x)/x^2`

If f (x)= |{:(x cos x, 2x sin x, x tan x),(1,x,1),(1,2x,1):}|, find lim _(xto0) (f(x))/(x ^(2)).

Let f(x)=|cosx x 1 2sinx x2xsinx x x| , then (lim)_(x->0)(f(x))/(x^2) is equal to (a) 0 (b) -1 (c) 2 (d) 3

If f(x)=[(sinx,cosecx,tanx),(secx,xsinx,xtanx),(x^2-1,cosx,x^2+1)] then int_(-a) ^ a f(x) dx equals

f(x)=|{:(cos x, x, 1),(2sin x, x^(2), 2x),(tan x, x, 1):}|." Then find the vlue of lim_(x to 0) (f'(x))/(x).

Consider the function : f (x) ={(x+2, x ne 1),(0,x=1):} . To find lim_(x to 1) f(x) .

Consider the function : f(x)={{:(x+2",", x ne 1), (0",", x =1.):} To find lim_(x to 1)f(x) .

Consider the function f(x)=1-x,0<=x<=1 and f(x)=x+2,1

If f(x)={:{(2x+1,x le 0),(3(x+1),x gt 0):} . Find lim_(x to 0) f(x) and lim_(x to 1) f(x) .

f(x)+f(y)=f((x+y)/(1-xy)) ,for all x,yinR . (xy!=1) ,and lim_(x->0) f(x)/x=2 .Find f(1/sqrt3) and f'(1) .

f(x)+f(y)=f((x+y)/(1-xy)) ,for all x,yinR . (xy!=1) ,and lim_(x->0) f(x)/x=2 .Find f(1/sqrt3) and f'(1) .