Find number of roots of f(x) where `f(x) = 1/(x+1)^3 -3x + sin x`

Find lim_(x to 1) f(x) , where f(x) = {{:(x + 1, x != 1),(0, x = 1):}}

In f (x)= [{:(cos x ^(3),, x lt 0), ( sin x ^(3) -|x ^(3)-1|,, x ge 0):} then find the number of points where g (x) =f (|x|) is non-differentiable.

If f (x)=((x-1) (x-2))/((x-3)(x-4)), then number of local extemas for g (x), where g (x) =f (|x|):

If f(x-1)=f(x+1) , where f(x)=x^2-2x+3 , then: x=

Find 'a' if f^(')(a)=0 , where f(x)=x^(3)-3x^(2)+3x-1

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