Question 11 Find the length of the curve with parametric equations x = 2t, y =...
please answer both (12(8 pts) Find parametric equations of the line through the point (2, -1,3) and perpendicular to the line with parametric equations 1-t,y 4- 2t and 3+ t and perpendicular to the line with parametric equations 3+t,y 2-t and z 3+2t. (13)(8 pts) Find the unit tangent vector (T(t) for the vector function r(t) - costi+3t j+ 2sin 2t k at the point where t 0 (12(8 pts) Find parametric equations of the line through the point (2,...
Consider the parametric equations below. x = 2 + 4t y = 1-t2 (a) Sketch the curve by using the parametric equations to plot points. Indicate with an arrow the direction in which the curve is traced as t increases.(b) Eliminate the parameter to find a Cartesian equation of the curve. y = _______ Consider the parametric equations below. x = 3t - 5 y = 2t + 4 (a) Sketch the curve by using the parametric equations to plot points. Indicate with an arrow the...
Question 11 Find the constanta if the length of the curve given by the parametric equations is 47 = a cost, y= a sint; osts
Consider the parametric curve given by x(t) = 16 sin3(t), y(t) = 13 cos(t) − 5 cos(2t) − 2 cos(3t) − cos(4t), where t denotes an angle between 0 and 2π. (a) Sketch a graph of this parametric curve. (b) Write an integral representing the arc length of this curve. (c) Using Riemann sums and n = 8, estimate the arc length of this curve. (d) Write an expression for the exact area of the region enclosed by this curve.
(6pts) Consider the curve given by the parametric equations x = cosh(4t) and y = 4t + 2 Find the length of the curve for 0 <t<1 M Length =
Question 15 < > Find the length of the curve for the following parametric equations for 2 <t < 10. Find its exact value, no decimals. r(t) = e' - 36 ly(t) = 2461/2 Length =
Find the Derivative of a Curve Defined by Trigonometric Parametric Equations Question What are the critical points for the plane curve defined by the equations r(t)o(2)(t)1in(2t), and t<T? Write your answer as a list of values of t, separated by commas. For example, if you found t 1 ort would enter 1,2. 2, you Provide your answer below: Find the Derivative of a Curve Defined by Trigonometric Parametric Equations Question What are the critical points for the plane curve defined...
For the following equations : x= 2t^2 , y = 3t^2 , z= 4t^2 ; 1 <=t <=3 A) write the position vector and tangent vector for the curve with the parametric equations above B) Find the length function s (t) for the curve C) write the position vector as a function of s and verify by differentiation that this position vector in terms of s is a unit tangent to the curve.
(1 point) Find the length of the curve defined by the parametric equations 3 -1, X = y = 3 ln((t/4)2 – 1) from t = 6 to t = 7.
uestion 7[value16jp (a) Find parametric equations for the tangent line to the curve of intersection of the cvlinders y -r2 and z - r2 at the point (1, -1,1) (b) Find an equation for the osculating plane of the curve ア(t) 〈cos 3t, 4t, sin 3t) at the point (-1.4T,0). uestion 7[value16jp (a) Find parametric equations for the tangent line to the curve of intersection of the cvlinders y -r2 and z - r2 at the point (1, -1,1) (b)...