Let C be the parametric curve defined by Sx(t) = t2 – t – 2, |v(t) = t* – º +t. Determine if C is concave up or concave down at 3 -2,
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- 1. Let C be the parametric curve defined by x(t) = t2 - 2; y(t) = t3 - 3t + 1: Determine if C is concave up or concave down at (-1; 3):Find a parametric description for the curve y=4-x^2 from (-2, 0) to (2, 0) such that t=0 corresponds to (-2, 0)Consider the curve C parametrized byx = (t^2+1)/(t^2-1) and y = (2t)/(t^2-1) for all t in (−∞, −1 ) ∪ (−1, 1) ∪ (1, ∞) .By squaring both x and y, find an equation of C in terms of just x and y (no t):
- 1. If the parametric curve $x=f(t), y=g(t)$ satisfies $g^{\prime}(1)=0,$ then it has a horizontal tangent when $t=1$Sketch the space curve r(t) = ⟨2 sin t, 5t, 2 cos t⟩ and find its length over the given interval [0, π] .Find, in the standard y = mx + b form, the tangent line to the parametric curve( 1/(t^2 +1) , 1/t) at the point ( 1/2 , 1)
- TRUE OR FALSE. A plane curve C defined by the parametric equations x = f(t) and y = g(t), where t is in the closed interval [a,b], is said to be smooth if f'(t) and g'(t) are not both zero at every number in the open interval (a,b).Show that the parametric curve r(t)= <(t/sqrt(1+t^2), 1/sqrt(1+t^2)> , t [-1,1] is smooth and compute its lenghuse the given graphs of x = ƒ(t) and y = g(t) to sketch the corresponding parametric curve in the xy-plane.