If a function is represented parametrically be the equations `x=(1+(log)_e t)/(t^2); y=(3+2(log)_e t)/t ,` then which of the following statements are true?

A function is reprersented parametrically by the equations x=(1+t)/(t^3); y=3/(2t^2)+2/t then the value of |(dy)/(dx)-x((dy)/(dx))^3| is__________

If x=sin t and y=cos p t , then which of the following is true ?

Separate the intervals of monotonocity for the function f(x)=((log)_e x)^2+((log)_e x)

Find the equation to the locus represented by the parametric equations x=2t^(2)+t+1, y=t^(2)-t+1 .

Computing area with parametrically represented boundaries : If the boundary of a figure is represented by parametric equation, i.e., x=x(t), y=(t), then the area of the figure is evaluated by one of the three formulas : S=-int_(alpha)^(beta)y(t)x'(t)dt, S=int_(alpha)^(beta)x(t)y'(t)dt, S=(1)/(2)int_(alpha)^(beta)(xy'-yx')dt, Where alpha and beta are the values of the parameter t corresponding respectively to the beginning and the end of the traversal of the curve corresponding to increasing t. The area of the loop described as x=(t)/(3)(6-t),y=(t^(2))/(8)(6-t) is

Computing area with parametrically represented boundaries : If the boundary of a figure is represented by parametric equation, i.e., x=x(t), y=(t), then the area of the figure is evaluated by one of the three formulas : S=-int_(alpha)^(beta)y(t)x'(t)dt, S=int_(alpha)^(beta)x(t)y'(t)dt, S=(1)/(2)int_(alpha)^(beta)(xy'-yx')dt, Where alpha and beta are the values of the parameter t corresponding respectively to the beginning and the end of the traversal of the curve corresponding to increasing t. The area of the region bounded by an are of the cycloid x=a(t-sin t), y=a(1- cos t) and the x-axis is

Computing area with parametrically represented boundaries : If the boundary of a figure is represented by parametric equation, i.e., x=x(t), y=(t), then the area of the figure is evaluated by one of the three formulas : S=-int_(alpha)^(beta) y(t)x'(t)dt, S=int_(alpha)^(beta) x(t)y'(t)dt, S=(1)/(2)int_(alpha)^(beta)(xy'-yx')dt, Where alpha and beta are the values of the parameter t corresponding respectively to the beginning and the end of the traversal of the curve corresponding to increasing t. If the curve given by parametric equation x=t-t^(3), y=1-t^(4) forms a loop for all values of t in [-1,1] then the area of the loop is

Area enclosed by the curve y=f(x) defined parametrically as x=(1-t^2)/(1+t^2), y=(2t)/(1+t^2) is equal

Find y_2 in each of the following cases: x=e^t,y=sint at t=pi/2

Find the derivatives w.r.t. x : x=t log t, y=(log t)/(t)" when " t =1