" If "|x|<1" and "y=1+x+x^(2)+x^(3)+...," then write the value of "(dy)/(dx)

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

Solve for x: |[x,c+x,b+x],[c+x,x,a+x],[b+x,a+x,x]|=0

Solve for x: |(x+9,x,x),(x,x+9,x),(x,x,x+9)|=0

(1) If | [a+x ,a ,x ],[a-x, a ,x], [a-x, a ,-x] |=0 then x is

|{:(" "x," "c+x," "b+x),(" "c+x," "x," "a+x),(" "b+x," "a+x," "x):}|=0

If |(a+x, a-x, a-x),(a-x,a+x,a-x),(a-x,a-x,a+x)|=0 then

If f(x)=|{:(1,x,x+1),(2x,x(x-1),(x+1)x),(3x(x-1),x(x-1)(x-2),(x+1)x(x-1)):}| then

Using the properties of determinants, solve the following for x |{:(a+x,a-x,a-x),(a-x,a+x,a-x),(a-x,a-x,a+x):}|=0

Using properties of determinants, solve for x:|[a+x, a-x, a-x],[ a-x, a+x, a-x],[ a-x, a-x, a+x]|=0