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)` . If `("lim")_(avec0)=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

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 ……………

Points (-4,0) and (7,0) lie on x-a xi s (b) y-a xi s in first quadrant (d) In second quadrant

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

For the curve y^(n)=a^(n-1)x if the subnormal at any point is a constant, then n is equal to

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

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 :

lim_ (n rarr oo) (n ^ (alpha) sin ^ (2) n!) / (n + 1), 0

If the sub-normal at any point on y=a^(1-n)x^(n) is of constant length,then find the value of n .