1. Curve (2a-X) = x '. (Jabalpur 2010.-

The asymptote to the curve y^(2)(2 + x) = x^(2) (6 - x) is

The slope of the tangent to a curve, y = f(x) at (x, f(x)) is 2x+1. If the curve passes through the point (1,2) , then the area of the region bounded by the curve, the x -axis and the line x=1

Given 3x^(2) +x=1 , find the value of 6x^(3) - x^(2) -3x + 2010 .

If 2010 is a root of x^(2)(1 - pq) - x(p^(2) + q^(2)) - (1 + pq) = 0 and 2010 harmonic mean are inserted between p and q then the value of (h_(1) - h_(2010))/(pq(p - q)) is

If 2010 is a root of x^(2)(1 - pq) - x(p^(2) + q^(2)) - (1 + pq) = 0 and 2010 harmonic mean are inserted between p and q then the value of (h_(1) - h_(2010))/(pq(p - q)) is

If (3+x^(2008)+x^(2009))^(2010)=a_0+a_1x+a_2x^2++a_n x^n , then the value of a_0-1/2a_1-1/2a_2+a_3-1/2a_4-1/2a_5+a_6- is a. 3^(2010) b. 1 c. 2^(2010) d. none of these

The slope of the tangent to a curve y=f(x) at (x,f(x)) is 2x+1. If the curve passes through the point (1,2) then the area of the region bounded by the curve, the x-axis and the line x=1 is

Sketch the curves and identify the region bounded by the curves x=(1)/(2),x=2,y=log x an y=2^(x). Find the area of this region.