" Let "f(x)=|[cos x,x,1],[2sin x,x^(2),2x],[tan x,x,1]|" then equation of normal drawn at "x=0" is "

let f(x)=det[[cos x,x,12sin x,x^(2),2xtan x,x,1]]. then lim_(x rarr0)(f'(x))/(x)=

f'(x) = |{:(cos x , x , 1),(2sin x,x^(2),2x),(tan x, x,1):}| . The value of underset(x rarr 0)(lim) (f(x))/(x) is equal to

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).

Let (x)=|[cos x,2sin x,sin x],[x,x,x],[1,2x,x]|," then "lim_(x rarr0)(f(x))/(x^(2) is equal

" If "f(x)=|[x,sin x,cos x],[x^(2),tan x,-x^(3)],[2x,sin2x,5x]|" ,then "lim_(x rarr0)(f'(x))/(x)=

If y=(1+x)^(2y)+cos^2(sin^(-1)x) be a curve then find equation of normal at x=0 .

Let f(x)={|x| if 0<=x<=2sin^(2)x+tan x if 2

Let f(x)=1+2sin x+2cos^(2)x,0<=x<=(pi)/(2) then

Let f(x)=|(cos x,e^(x^2) , 2x cos^2x/2),(x^2, sec x, sinx+x^3),(1,2,x+tan x)| then the value of int_(-pi/2)^(pi/2)(x^2+1)(f(x)+f''(x))dx