" 7.) "3(t-3)=5(2t+1)quad " 8."quad 15(y-4)-2(y-9)+5(y+6)=0

If u=sin^(-1)(x-y),x=3t,y=4t^(3) , then what is the derivative of u with respect to t? (A) 3(1-t^2) (B) 3(1-t^2)^(-1/2) (C) 5(1-t^2)^(-1/2) (D) 5(1-t^2)

The equation of the tangent to the curve x = (t - 1)/(t + 1), y = (t + 1)/(t - 1) at t = 2 is a) x + 9y - 6 = 0 b) 9x - y - 6 = 0 c) 9x + y + 6 = 0 d) 9x + y - 6 = 0

The equation of normal to the curve x=(1)/(t), y=t-(1)/(t)" at "t=2 is: a)x+5y+7=0 b)5x+y+7=0 c)x-5y+7=0 d)5x-y+7=0

Verify whether the following are true or false . (i) -3 is a zero of x-3 (ii) -(1)/(3) is a zero of 3x+1 (iii) -(4)/(5) is a zero of 4-5y (iv) 0 and 2 are the zeroes of t^(2) -2t (v) -3 is a zero of y^(2)+y-6

Verify whether the following are true or false . (i) -3 is a zero of x-3 (ii) -(1)/(3) is a zero of 3x+1 (iii) -(4)/(5) is a zero of 4-5y (iv) 0 and 2 are the zeroes of t^(2) -2t (v) -3 is a zero of y^(2)+y-6

Let the function y = f(x) be given by x= t^(5) -5t^(3) -20t +7 and y= 4t^(3) -3t^(2) -18t + 3 where t in ( -2,2) then f'(x) at t = 1 is

Let the function y = f(x) be given by x= t^(5) -5t^(3) -20t +7 and y= 4t^(3) -3t^(2) -18t + 3 where t in ( -2,2) then f'(x) at t = 1 is

Find the equations of the tangent and normal to the given curves at the indicated points: (i) y=x^4-6x^3+13 x^2-10 x+5 at (0," "5) (ii) y=x^4-6x^3+13 x^2-10 x+5 at (1," "3) (iii) y=x^3 at (1," "1) (iv) y=x^2 at (0," "0) (v) x" "=" cos t ,y=sin t ""at "" t=pi/4