Given a curve defined by the parametric equations (t) = t³, y(t) = t², for t € R, find the curvature of the curve at t = 1.
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- Use the graphs of x=f(t) and y=g(t) to sketch the parametric curve x= f(t), y=g(t). Indicate with arrows the direction in which the curve is traced as t increases.Consider the parametric curve x = 1² – 2t, y = t³ — 3t²2 + 2t. Find the equations of the tangent lines to the curve at all x-intercepts (i.e. points (x, 0) that cross the x-axis).Sketch the curve given by the parametric equations x= t³ - 1 and y= t² + t. Construct a table with three constants: t, x(t) and y(t)Evaluate x and y for values of t over the interval for which the functions are defined.Plot the resulting pairs (x, y).
- Consider the parametric curve C: x=1+cost, y= -3+2sint, 0 stS (1) Sketch the curve and indicate the orientation of the curve TO (2) Find the equation of the tangent line when t= 6.For the smooth curve r(t) find the parametric equations for the line tangent to r at the given value of t.Consider the curve described by the parametric equations ¤ = t² +4 and y = 3t + 4t. Determine the slope of the tangent line to the curve when t = 1. Enter your answer as an exact value in decimal form.
- Find the equation for the line tangent to the parametric curve: at the points where t = 2 and t = -2. For t = 2, the tangent line (in form y = mx + b) is y = For t= -2, the tangent line is y = 8 Y = = t³-4t 4t²t4Use the graphs of x = f(t) and y = g(t) to sketch the parametric curve x = f(t), y = g(t). Indicate with arrows the direction in which the curve is traced as t increases. XA -1 У У х х -2 -1 -2 -1 -2- -2- х -2 -2 2. 2.Give the parametric curve: x = t3 - 6t2 y = t2 - 2t Find an equation for the line tangent at the point where x = 16 and t > 0.