[" If "|x|<1," then the sum of the series "],[1+2x+3x^(2)+4x^(3)+...........oo" Will be "]

" 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 |(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

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

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

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

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

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

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