`-39 x^4` by `sqrt(13) x^2`

If f(x)=cos^(-1)((1)/(sqrt(13)))(2cos x-3sin x)+sin^(-1)((1)/(sqrt(13)))(2cos x+3sin x)wdot rt sqrt(1+x^(2)) then find (df(x))/(dx) at x=(3)/(4)

The distance of the point (2,1,-1) from the plane x-2y+4z=9 is (A) sqrt(13)/21 (B) 13/21 (C) 13/sqrt(21) (D) sqrt(13/21)

The distance of the point (2,1,-1) from the plane x-2y+4z=9 is (A) sqrt(13)/21 (B) 13/21 (C) 13/sqrt(21) (D) sqrt(13/21)

Domain of f(x) = sqrt(2x-1) + sqrt(13) cos^(-1) ((2x-1)/2) is

If int sin^-1 ((2x + 2)/sqrt(4x^2 + 8x + 13)) dx = (x + 1) tan^-1 ((2x+2)/3) + lambda In (4x^2 + 8x + 13) + c , then the value of -4lambda must be

If x = sqrt(13)+2sqrt(3) , find the value of x-(1)/(x) .

The length of latusrectum of the parabola 13[(x-3)^(2)+(y-4)^(2)]=(2x-3y+5)^(2) is A) (2)/(sqrt(13)) B) (4)/(sqrt(13)) C) (1)/(sqrt(13)) D) (5)/(sqrt(13))

If (sqrt(2))^(x)+(sqrt(3))^(x)=(sqrt(13))^(x//2) , then the number of real values of x is