If `f(x)=2/(sqrt(3))tan^(-1)((2x+1)/(sqrt(3)))-log(x^2+x+1)(lambda^2-5lambda+3)x+10` is a decreasing function for all `x in R ,` find the permissible values of `lambdadot`

If the equation (5x-1)^2+(5y-2)^2=(lambda^2-2lambda+1)(3x+4y-1)^2 represents an ellipse, then find values of lambdadot

f(x)=sqrt(x^(2)+1) then lim_(xto3)(f(x)-sqrt(10))/(x-3) is

If alpha=tan^(-1)((sqrt(3)x)/(2y-x)),beta=tan^(-1)((2x-y)/(sqrt(3y)))" then "alpha-beta=

If f(x)=3sqrt(1−x^2)​+3sqrt(1−x^2)​, then f(x) is

Evaluate lim_(xto1) ((2x-3)(sqrt(x)-1))/(2x^(2)+x-3).

The function f (x) = log (x + sqrt(x^2 +1)) is

"Let "f(x)=((2^(x)+2^(-x))sin x sqrt(tan^(-1)(x^(2)-x+1)))/((7x^(2)+3x+1)^(3)) . Then find the value of f'(0).

If f(x)=x^3+4x^2+lambdax+1 is a monotonically decreasing function of x in the largest possible interval (-2,-2/3)dot Then (a ) lambda=4 (b) lambda=2 (c) lambda=-1 (d) lambda has no real value

if: f(x)=(sinx)/(sqrt(1+tan^2x))-(cosx)/(sqrt(1+cot^2x)), then find the range of f(x)