Evaluate the following using :L ' Hospital 's rule . (i) if f(x) be a twice differentiable function and f'' (0) =2 , then find underset(x to 0) lim (2f(x)-3f(3x)+f(4x))/x^(2) (ii) if f(a) =2, f' (a) = 1, g (a) =2 , then find underset(x to 0) (g(x)f(a) -g(a)f(x0))/(x-a) (iii) underset( x to 0) (1/x - 1 /(sin x) ) (iv) lim(x to 0+) x In x (v) underset(x to 0) | cot x|^( sin x) (vi) underset(x to 0) (tan x + 4 tan 2x -3 tan 3x)/(x^(2) tan x)
Let f(x)=|x^(2)-4x+3|ln x+2(x-2)^((1)/(3))x>0h(x)=x-1;x in Q;x^(2)-x-2;x neg in Qf(x) is non differentiable at points and the sum of corresponding x value(s) is
If f(x)={x^(2)+3x+a,quad f or x is everywhere differentiable,find the values of a and b
If f(x)={x^(3),x^(2) =1 then f(x) is differentiable at
If f(x) = f(1 - x) and f(x) is differentiable are every real value of x then the value of f' ((1)/(2)) + f' ((1)/(4)) + f' ((3)/(4)) is _____
