The points of the curve y = x3 + x - 2 at which its tangent are parallel to the straight line y = 4x - 1 are
(2, 7), (- 2, - 11)
(0, 2), (21/3, 21/3)
(- 21/3, - 21/3), (0, - 4)
(1, 0), (- 1, - 4)
The equation of the normal to the curve y = - + 2 at the point of its intersection with the bisector of the first quadrant is
4x - y + 16 = 0
4x - y = 16
2x - y - 1 = 0
2x - y + 1 = 0
The angle at which the curve y = x2 and the curve x = , y = intersect is
B.
Which is parametnc equation, we change this equation is cartesian equation as follows
On squaring and adding both i.e. cos(t) and sin(t), we get
The intersection points at Eq. (i) and (iii) are (1, 1) and (- 1, 1)
Now, slope of tangent of Eq. (i) at point (1, 1) is
And slope of tangent of Eq (iii), at point (1, 1) is
Angle at point of intersection of Eqs. (i) and (iii), we get
Similarly, slope of tangent of Eq. (i) at point (- 1, 1)
And slope of tangent of Eq (iii) at point (-1, 1)
Angle at point of intersection of Eqs. (i) and (iii), we get
The function f(x) = , f(0) = 0 is
differentiable at x = 0
neither continuous at x = 0 nor differentiable at x = 0
not continuous at x = 0
continuous at x = 0 but not differentiable at x = 0
The values of a and b for which the function y = aloge(x ) + bx2 + x, has extremum at the points x1 = 1 and x2 = 2 are
The tangent to the graph of a continuous function y = f(x) at the point with abscissa x = a forms with the X-axis an angle of and at the point with abscissa x = b an angle of , then what the value of integral
(where f'(x) the derivative off w.r.t. xwhich is assumed to be continuous and similarly f"(x) the double derivative of f w.r.t. x)
eb +
A closed figure S is bounded by the hyperbola x2 - y2 = a2 and the straight line x = a + h; (h > 0, a > 0). This closed figure is rotated about the X-axis. Then, the volume of the solid ofrevolution is