Test: Basic Concepts Of Differential And Integral Calculus- 1

If y = x (x –1) (x – 2) then  is

The gradient of the curve y – xy + 2px + 3qy = 0 at the point (3, 2 ) is and q are

The curve y² = ux³ + v passes through the point P(2, 3) and  = 4 at P. The values of u and v are 

The gradient of the curve y + px +qy = 0 at (1, 1) is 1/₂. The values of p and q are

If xy = 1 then y² + dy/dx is equal to

The derivative of the function 

Given e^-xy –4xy = 0,  can be proved to be

If log (x / y) = x + y,   may be found to be

If f(x, y) = x³ + y³ – 3axy = 0,  can be found out as

Given x = at², y = 2at;  is calculated as

Given x = 2t + 5, y = t² – 2;  is calculated as 

If y = 

If x = 3t² –1, y = t³ –t, then   is equal to

The slope of the tangent to the curve y = at the point, where the ordinate and the abscissa are equal, is

The slope of the tangent to the curve y = x² –x at the point, where the line y = 2 cuts the curve in the Ist quadrant, is

For the curve x² + y² + 2gx + 2hy = 0, the value of  at (0, 0) is

If x^y.y^x = M, M is constant then is equal to

Given x = t + t^–1 and y = t – t^–1 the value of  at t = 2 is

If x³ –2x² y² + 5x +y –5 =0 then  at x = 1, y = 1 is equal to

The derivative of x² log x is

The derivative of 

If f(x) = 3x², then F(x) = 

If f(x) = x² – 6x+8 then f ’(5) – f ’(8) is equal to

If f(x) = x^k and f’(1) = 10 the value of k is