At the point `P(a,a^(n))` on the graph of `y=x^(n)(n in N)` in the first quadrant at normal is drawn. The normal intersects the Y-axis at the point (0, b). If `underset(ararr0)(lim)b=(1)/(2)`, then n equals ……………

At the point P(a,a^(n)) on the graph of y=x^(n)(n in N) in the first quadrant at normal is drawn. The normal intersects the Y-axis at the point (0, b). If lim_(ararr0)b=(1)/(2) , then n equals ……………

At the point P(a,a^(n)) on the graph of y=x^(n),(n in N), in the first quadrant,a normal is drawn.The normal intersects the y- axis at the point (0,b).. If lim_(a rarr0)=(1)/(2), then n equals

At the point P(a , a^n) on the graph of y=x^n ,(n in N), in the first quadrant, a normal is drawn. The normal intersects the y-a xi s at the point (0, b)dot If ("lim")_(avec0)b=1/2, then n equals 1 (b) 3 (c) 2 (d) 4

Consider the curve y=x^n where n > 1 in the 1^st quadrant. Ifthe areabounded by the curve, the x-axis and the tangent line to the graph of y=x^n at the point (1, 1) is maximum then find the value of n.

If the points A(3,\ 5)a n d\ B(1,\ 4) lie on the graph of the line a x+b y=7, find the values of a\ a n d\ b

The slope of normal to the curve x^(3)=8a^(2)y, a gt 0 at a point in the first quadrant is -(2)/(3) , then point is

Let F_1(x_1,0) and F_2(x_2,0), for x_1 0, be the foci of the ellipse x^2/9+y^2/8=1 Suppose a parabola having vertex at the origin and focus at F_2 intersects the ellipse at point M in the first quadrant and at point N in the fourth quadrant. If the tangents to the ellipse at M and N meet at R and the normal to the parabola at M meets the x-axis at Q, then the ratio of area of the triangle MQR to area of the quadrilateral MF_1 NF_2 is

The tangent to the hyperbola xy=c^2 at the point P intersects the x-axis at T and y- axis at T'.The normal to the hyperbola at P intersects the x-axis at N and the y-axis at N' . The areas of the triangles PNT and PN'T' are Delta and Delta' respectively, then 1/Delta+1/(Delta)' is (A) equal to 1 (B) depends on t (C) depends on c D) equal to 2

For 0 lt r lt 1, let n_(r) dennotes the line that is normal to the curve y = x ^® at the point (1,1) Let S _(r) denotes the region in the first quadrant bounded by the curve y = x ^(r ) ,the x-axis and the line n _(r )' Then the value of r the minimizes the area of S_(r ) is :