Points on the curve `f(x)=x/(1-x^2)` where the tangent is inclined at an angle of `pi/4` to the x-axis are (0,0) (b) `(sqrt(3),-(sqrt(3))/2)` `(-2,2/3)` (d) `(-sqrt(3),(sqrt(3))/2)`

Points on the curve f(x)=(x)/(1-x^(2)) , where the tangent is inclined at an angle of (pi)/(4) to x-axis, are

If at each point of the curve y=x^3-a x^2+x+1, the tangent is inclined at an acute angle with the positive direction of the x-axis, then (a) a >0 (b) a<-sqrt(3) (c) -sqrt(3)< a < sqrt(3) (d) non eoft h e s e

The abscissas of point Pa n dQ on the curve y=e^x+e^(-x) such that tangents at Pa n dQ make 60^0 with the x-axis are. (a)1n((sqrt(3)+sqrt(7))/7)a n d1n((sqrt(3)+sqrt(5))/2) (b)1n((sqrt(3)+sqrt(7))/2) (c)1n((sqrt(7)-sqrt(3))/2) (d)+-1n((sqrt(3)+sqrt(7))/2)

4 cos^(2)x + sqrt(3) = 2(sqrt(3)+1)

sqrt(3)x^(2) - sqrt(2)x + 3sqrt(3)=0

The point on the parabola y^(2) = 8x at which the normal is inclined at 60^(@) to the x-axis has the co-ordinates as (a) (6,-4sqrt(3)) (b) (6,4sqrt(3)) (c) (-6,-4sqrt(3)) (d) (-6,4sqrt(3))

If tan^(-1)x+2cot^(-1)x=(2pi)/3, then x , is equal to (a) (sqrt(3)-1)/(sqrt(3)+1) (b) 3 (c) sqrt(3) (d) sqrt(2)

int (dx)/(sqrt(1+sqrt(x)))=(4)/(3)(sqrt(x)-2)sqrt(1+sqrt(x))+c

A function g(x) is defined as g(x)=1/4f(2x^2-1)+1/2f(1-x^2) and f(x) is an increasing function. Then g(x) is increasing in the interval. (a) (-1,1) (b) (-sqrt(2/3),0)uu(sqrt(2/3),oo) (c) (-sqrt(2/3),sqrt(2/3)) (d) none of these

Find the value of x : (sqrt(3)+sqrt(2))^(x)+(sqrt(3)-sqrt(2))^(x)=10