The tangent to the curve `y=e^(k x)` at a point (0,1) meets the x-axis at (a,0), where `a in [-2,-1]` . Then `k in ` `[-1/2,0]` (b) `[-1,-1/2]` `[0,1]` (d) `[1/2,1]`

The equation of the tangent tothe curve y={x^2 sin(1/x),x!=0 and 0, x=0 at the origin is

If the tangent to the curve x y+a x+b y=0 at (1,1) is inclined at an angle tan^(-1)2 with x-axis, then find aa n db ?

The slope of the tangent to the curve y=sqrt(4-x^2) at the point where the ordinate and the abscissa are equal is -1 (b) 1 (c) 0 (d) none of these

Find the acute angle between the curves y=x^(2) and x=y^(2) at their points of intersection (0,0), (1,1) .

If the tangent at (1,1) on y^2=x(2-x)^2 meets the curve again at P , then find coordinates of P

The domain of f(x)=sqrt(2{x}^2-3{x}+1), where {.} denotes the fractional part in [-1,1] is (a) [-1,1]-(1/(2,1)) (b) [-1,-1/2]uu[(0,1)/2]uu{1} (c) [-1,1/2] (d) [-1/2,1]

Find the length of the tangent for the curve y=x^3+3x^2+4x-1 at point x=0.

The curve given by x+y=e^(x y) has a tangent parallel to the y- axis at the point (a) (0,1) (b) (1,0) (c) (1,1) (d) none of these

If the tangent to the curve, y = x^(3) + ax -b at the point (1, -5) is perpendicular to the line, -x +y + 4 =0 , then which one of the following points lies on the curve ? (A) (-2, 2) (B) (2, -2) (C) (-2, 1) (D) (2, -1)