The derivative of the function represented parametrically as `x=2t=|t|,y=t^3+t^2|t|a tt=0` is a. -1 b. 1 c. 0 d. does not exist

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

The vertex of the parabola whose parametric equation is x=t^2-t+1,y=t^2+t+1; t in R , is

Let y=f(x) be defined parametrically as y=t^2+t|t|, x=2t-|t|, t in R , Discuss its continuity.

Consider a function y = f(x) defined parametrically as y=2t+t, x=t^2 foralltin R then the function f(x) 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

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 curve is represented parametrically by the equations x=f(t)=a^(In(b'))and y=g(t)=b^(-In(a^(t)))a,bgt0 and a ne 1, b ne 1" Where "t in R. The value of f(t)/(f'(t))cdot(f''(-t))/(f'(-t))+(f(-t))/(f'(-t))cdot(f''(t))/(f'(t))AA t in R 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 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