The parametric equations of a curve is x = = 3 sint, y = 3 cost and z = 4. (a) Sketch the curve r(t) for 0 ≤ t ≤ 2. (b) Find the followings when t = 0: (i) The unit tangent vector, T. (ii) The principal unit normal, N.

Q: (a) Find an equation of the tangent(s) to the curve at the given point. x = t³-t, y = e²t + 3t+2;…

A: We will find the required.

Q: Find an equation, in slope-intercept form, of the line tangent to the curve with parametric…

A:

Q: Consider the parametric curve C: x 1+cost, y= -3+2sint, 0stS (1) Sketch the curve and indicate the…

A:

Q: x=sec(t) y=tan(t) t E[0,pi] a) Identitfy the (x,y) coordinates of the point corresponding to the…

A: To determine the coordinates of the point.

Q: For the parametric curve given by x = t + sin 2t, y = cos 2t, dy d²y (i) calculate the derivatives…

A: Given parametric equations: Objective: To calculate the derivative of and .To find the equation of…

Q: 1 cos(t) - 2 sin(t) Find the slope of the tangent line to the parametric curve at the point

A:

Q: Sketch the graph defined by the parametric equations x = e' -t and y = 4e? for 0st<2. Indicate on…

A:

Q: Consider the parametric curve defined by x = 2020 cos t y = 2020 sin t π Find the slope of this…

A: Slope of a curve at some point is the value of the derivative at that point.

Q: What are some of the advantages of expressing a curve parametrically rather than in the form y =…

A: Given that the parametric equation.

Q: Find for the parametric curve x= 2e', y= sin(1+ e') dx

A:

Q: The curve defined by any parametric equations X = f(t), y = g(t) is always a function.

A:

Q: 3. A curve has parametric equations r = sin(3t) and y = cos(t) where t takes all real %3D values. dy…

A:

Q: JUIR tO JusLily your aASWers. Witë your solutions properly, heatly, and carefully answers as much as…

A:

Q: Find parametric equations for the line that is tangent to the given curve at the given parameter…

A:

Q: x = 1 cos(t) y = 2 sin(t) Find the slope of the tangent line to the parametric curve at the point

A: